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Ulam Stability Of Operators

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Ulam Stability of Operators

Ulam Stability of Operators Book
Author : Janusz Brzdek,Dorian Popa,Ioan Rasa,Bing Xu
Publisher : Academic Press
Release : 2018-01-04
ISBN : 9780128098295
Language : En, Es, Fr & De

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Book Description :

6. Difference equation with a matrix coefficient -- 7. Linear functional equations with constant coefficients -- 8. Linear differential equations -- 9. Integral equations -- References -- CHAPTER 6: Nonstability theory -- 1. Preliminary information -- 2. Possible definitions of nonstability -- 3. Linear difference equation of the first order -- 4. Linear difference equation of a higher order -- 5. Linear functional equation of the first order -- 6. Linear functional equation of a higher order -- References -- Index -- Back Cover

Ulam Stability of Operators

Ulam Stability of Operators Book
Author : Janusz Brzdek,Dorian Popa,Ioan Rasa,Bing Xu
Publisher : Academic Press
Release : 2018-01-10
ISBN : 0128098309
Language : En, Es, Fr & De

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Book Description :

Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations. Allows readers to establish expert knowledge without extensive study of other books Presents complex math in simple and clear language Compares, generalizes and complements key findings Provides numerous open problems

Ulam Type Stability

Ulam Type Stability Book
Author : Janusz Brzdęk,Dorian Popa,Themistocles M. Rassias
Publisher : Springer Nature
Release : 2019-10-29
ISBN : 3030289729
Language : En, Es, Fr & De

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Book Description :

This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research results on Ulam type stability of various classes of linear and nonlinear operators; in particular on the stability of many functional equations in a single and several variables (also in the lattice environments, Orlicz spaces, quasi-b-Banach spaces, and 2-Banach spaces) and some orthogonality relations (e.g., of Birkhoff–James). A variety of approaches are presented, but a particular emphasis is given to that of fixed points, with some new fixed point results and their applications provided. Besides these several other topics are considered that are somehow related to the Ulam stability such as: invariant means, geometry of Banach function modules, queueing systems, semi-inner products and parapreseminorms, subdominant eigenvalue location of a bordered diagonal matrix and optimal forward contract design for inventory. New directions and several open problems regarding stability and non-stability concepts are included. Ideal for use as a reference or in a seminar, this book is aimed toward graduate students, scientists and engineers working in functional equations, difference equations, operator theory, functional analysis, approximation theory, optimization theory, and fixed point theory who wish to be introduced to a wide spectrum of relevant theories, methods and applications leading to interdisciplinary research. It advances the possibilities for future research through an extensive bibliography and a large spectrum of techniques, methods and applications.

Frontiers in Functional Equations and Analytic Inequalities

Frontiers in Functional Equations and Analytic Inequalities Book
Author : George A. Anastassiou,John Michael Rassias
Publisher : Springer Nature
Release : 2019-11-23
ISBN : 3030289508
Language : En, Es, Fr & De

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Book Description :

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

Handbook of Functional Equations

Handbook of Functional Equations Book
Author : Themistocles M. Rassias
Publisher : Springer
Release : 2014-11-21
ISBN : 1493912860
Language : En, Es, Fr & De

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Book Description :

This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature. The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy–Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D’Alembert’s functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory.

Hyers Ulam Stability of Ordinary Differential Equations

Hyers Ulam Stability of Ordinary Differential Equations Book
Author : Arun Kumar Tripathy
Publisher : CRC Press
Release : 2021-05-24
ISBN : 1000386899
Language : En, Es, Fr & De

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Book Description :

Hyers-Ulam Stability of Ordinary Differential Equations undertakes an interdisciplinary, integrative overview of a kind of stability problem unlike the existing so called stability problem for Differential equations and Difference Equations. In 1940, S. M. Ulam posed the problem: When can we assert that approximate solution of a functional equation can be approximated by a solution of the corresponding equation before the audience at the University of Wisconsin which was first answered by D. H. Hyers on Banach space in 1941. Thereafter, T. Aoki, D. H. Bourgin and Th. M. Rassias improved the result of Hyers. After that many researchers have extended the Ulam's stability problems to other functional equations and generalized Hyer's result in various directions. Last three decades, this topic is very well known as Hyers-Ulam Stability or sometimes it is referred Hyers-Ulam-Rassias Stability. This book synthesizes interdisciplinary theory, definitions and examples of Ordinary Differential and Difference Equations dealing with stability problems. The purpose of this book is to display the new kind of stability problem to global audience and accessible to a broader interdisciplinary readership for e.g those are working in Mathematical Biology Modeling, bending beam problems of mechanical engineering also, some kind of models in population dynamics. This book may be a starting point for those associated in such research and covers the methods needed to explore the analysis. Features: The state-of-art is pure analysis with background functional analysis. A rich, unique synthesis of interdisciplinary findings and insights on resources. As we understand that the real world problem is heavily involved with Differential and Difference equations, the cited problems of this book may be useful in a greater sense as long as application point of view of this Hyers-Ulam Stability theory is concerned. Information presented in an accessible way for students, researchers, scientists and engineers.

Nonlinear Analysis Differential Equations and Applications

Nonlinear Analysis  Differential Equations  and Applications Book
Author : Themistocles M. Rassias
Publisher : Springer Nature
Release : 2021-08-20
ISBN : 3030725634
Language : En, Es, Fr & De

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Book Description :

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers–Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg–Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdős-Rényi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Functional Equations in Mathematical Analysis

Functional Equations in Mathematical Analysis Book
Author : Themistocles M. Rassias,Janusz Brzdek
Publisher : Springer Science & Business Media
Release : 2011-09-18
ISBN : 1461400554
Language : En, Es, Fr & De

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Book Description :

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.

Contributions in Mathematics and Engineering

Contributions in Mathematics and Engineering Book
Author : Panos M. Pardalos,Themistocles M. Rassias
Publisher : Springer
Release : 2016-10-04
ISBN : 3319313177
Language : En, Es, Fr & De

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Book Description :

The contributions in this volume aim to deepen understanding of some of the current research problems and theories in modern topics such as calculus of variations, optimization theory, complex analysis, real analysis, differential equations, and geometry. Applications to these areas of mathematics are presented within the broad spectrum of research in Engineering Science with particular emphasis on equilibrium problems, complexity in numerical optimization, dynamical systems, non-smooth optimization, complex network analysis, statistical models and data mining, and energy systems. Additional emphasis is given to interdisciplinary research, although subjects are treated in a unified and self-contained manner. The presentation of methods, theory and applications makes this tribute an invaluable reference for teachers, researchers, and other professionals interested in pure and applied research, philosophy of mathematics, and mathematics education. Some review papers published in this volume will be particularly useful for a broader audience of readers as well as for graduate students who search for the latest information. ​ Constantin Carathéodory’s wide-ranging influence in the international mathematical community was seen during the first Fields Medals awards at the International Congress of Mathematicians, Oslo, 1936. Two medals were awarded, one to Lars V. Ahlfors and one to Jesse Douglass. It was Carathéodory who presented both their works during the opening of the International Congress. This volume contains significant papers in Science and Engineering dedicated to the memory of Constantin Carathéodory and the spirit of his mathematical influence.

Infinite Products of Operators and Their Applications

Infinite Products of Operators and Their Applications Book
Author : Simeon Reich,Alexander J. Zaslavski
Publisher : American Mathematical Soc.
Release : 2015-03-30
ISBN : 1470414805
Language : En, Es, Fr & De

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Book Description :

This volume contains the proceedings of the workshop on Infinite Products of Operators and Their Applications, held from May 21-24, 2012, at the Technion-Israel Institute of Technology, Haifa, Israel. The papers cover many different topics regarding infinite products of operators and their applications: projection methods for solving feasibility and best approximation problems, arbitrarily slow convergence of sequences of linear operators, monotone operators, proximal point algorithms for finding zeros of maximal monotone operators in the presence of computational errors, the Pascoletti-Serafini problem, remetrization for infinite families of mappings, Poisson's equation for mean ergodic operators, vector-valued metrics in fixed point theory, contractivity of infinite products and mean convergence theorems for generalized nonspreading mappings. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).

Stability of Functional Equations in Banach Algebras

Stability of Functional Equations in Banach Algebras Book
Author : Yeol Je Cho,Choonkil Park,Themistocles M. Rassias,Reza Saadati
Publisher : Springer
Release : 2015-06-26
ISBN : 3319187082
Language : En, Es, Fr & De

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Book Description :

Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the latest results in mathematical analysis. Moreover, research mathematicians, physicists and engineers will benefit from the variety of old and new results, as well as theories and methods presented in this book.

Fractional Order Equations and Inclusions

Fractional Order Equations and Inclusions Book
Author : Michal Fečkan,JinRong Wang,Michal Pospíšil
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2017-11-07
ISBN : 3110521555
Language : En, Es, Fr & De

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Book Description :

This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Implicit Fractional Differential and Integral Equations

Implicit Fractional Differential and Integral Equations Book
Author : Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2018-02-05
ISBN : 311055318X
Language : En, Es, Fr & De

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Book Description :

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Absolutely Summing Operators

Absolutely Summing Operators Book
Author : Joe Diestel,Hans Jarchow,Andrew Tonge
Publisher : Cambridge University Press
Release : 1995-04-27
ISBN : 9780521431682
Language : En, Es, Fr & De

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Book Description :

This text provides the beginning graduate student with an account of p-summing and related operators.

Nonlinear Analysis

Nonlinear Analysis Book
Author : Panos M. Pardalos,Pando G. Georgiev,Hari M. Srivastava
Publisher : Springer Science & Business Media
Release : 2012-06-02
ISBN : 146143498X
Language : En, Es, Fr & De

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Book Description :

The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

Mathematical Analysis Approximation Theory and Their Applications

Mathematical Analysis  Approximation Theory and Their Applications Book
Author : Themistocles M. Rassias,Vijay Gupta
Publisher : Springer
Release : 2016-06-03
ISBN : 3319312812
Language : En, Es, Fr & De

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Book Description :

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Approximation and Computation in Science and Engineering

Approximation and Computation in Science and Engineering Book
Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer Nature
Release : 2022
ISBN : 3030841227
Language : En, Es, Fr & De

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Book Description :

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Statistical Properties of Deterministic Systems

Statistical Properties of Deterministic Systems Book
Author : Jiu Ding,Aihui Zhou
Publisher : Springer Science & Business Media
Release : 2010-06-28
ISBN : 3540853677
Language : En, Es, Fr & De

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Book Description :

Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.

Functional Analysis Approximation Theory and Numerical Analysis

Functional Analysis  Approximation Theory and Numerical Analysis Book
Author : John M Rassias
Publisher : World Scientific
Release : 1994-06-09
ISBN : 9814506052
Language : En, Es, Fr & De

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Book Description :

This book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards. Contents:On a Conditional Cauchy Equation on Rhombuses (C Alsina & J-L Carcia-Roig)Optimization of Functionals and Application to Differential Equations (P C Bhakta)On a Generalization of the Golab-Schinzel Functional Equation (N Brillouet-Belluot)On Shape from Shading Problem (J Chabrowski & K Zhang)Error Estimate in Non-Equi-Mesh Spline Finite Strip Method for Thin Plate Bending Problem (C Q Wu & Z H Wang)Asymptotic Behavior of Dynamical Systems and Processes on Banach Infinite Dimensional Spaces (A F Izé)Some Characterization Problems in Hilbert Space (R G Laha)On Banach Algebras of the Potential Differential and Pseudodifferential Operators (I E Pleshchinskaya & N E Pleshchinskii)On the Extended Ostrowski Constant (J M Rassias)An Interpretation of Gegenbauer Polynomials and Their Generalization for the Case with Many Variables (A Yanushauskas)The Uniqueness and Existence of Solution and Normal Boundary Condition for Thin Plate Bending Problem (Z H Wang & C Q Wu)Landau's Type Inequalities (J M Rassias)and other papers Readership: Students and researchers in mathematics. keywords:Functional Analysis;Approximation Theory;Numerical Analysis;Dedication

Topics in Mathematical Analysis and Applications

Topics in Mathematical Analysis and Applications Book
Author : Themistocles M. Rassias,László Tóth
Publisher : Springer
Release : 2014-10-13
ISBN : 3319065548
Language : En, Es, Fr & De

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Book Description :

This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.