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Theory Of Approximate Functional Equations

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Theory of Approximate Functional Equations

Theory of Approximate Functional Equations Book
Author : Madjid Eshaghi Gordji,Sadegh Abbaszadeh
Publisher : Academic Press
Release : 2016-03-03
ISBN : 012803971X
Language : En, Es, Fr & De

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Book Description :

Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors. In this book the authors investigate these developments in the theory of approximate functional equations. A useful text for graduate seminars and of interest to a wide audience including mathematicians and applied researchers Presents recent developments in the theory of approximate functional equations Discusses the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups

Handbook of Functional Equations

Handbook of Functional Equations Book
Author : Themistocles Rassias
Publisher : Springer
Release : 2016-09-10
ISBN : 9781493953097
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.

Approximation Theory and Analytic Inequalities

Approximation Theory and Analytic Inequalities Book
Author : Themistocles M. Rassias
Publisher : Springer Nature
Release : 2021-07-21
ISBN : 3030606228
Language : En, Es, Fr & De

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Book Description :

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

The Lerch zeta function

The Lerch zeta function Book
Author : Antanas Laurincikas,Ramunas Garunkstis
Publisher : Springer Science & Business Media
Release : 2013-12-11
ISBN : 9401764018
Language : En, Es, Fr & De

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Book Description :

The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students.

An Introduction to the Theory of the Riemann Zeta Function

An Introduction to the Theory of the Riemann Zeta Function Book
Author : S. J. Patterson
Publisher : Cambridge University Press
Release : 1995-02-02
ISBN : 131658335X
Language : En, Es, Fr & De

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Book Description :

This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number theory. Since then many other classes of 'zeta function' have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.

The Riemann Zeta Function

The Riemann Zeta Function Book
Author : Aleksandar Ivic
Publisher : Courier Corporation
Release : 2012-07-12
ISBN : 0486140040
Language : En, Es, Fr & De

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Book Description :

This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.

Developments in Functional Equations and Related Topics

Developments in Functional Equations and Related Topics Book
Author : Janusz Brzdęk,Krzysztof Ciepliński,Themistocles M. Rassias
Publisher : Springer
Release : 2017-08-23
ISBN : 9783319617312
Language : En, Es, Fr & De

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Book Description :

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Approximation Theory in Tensor Product Spaces

Approximation Theory in Tensor Product Spaces Book
Author : William A. Light,Elliot W. Cheney
Publisher : Springer
Release : 2006-11-14
ISBN : 3540397418
Language : En, Es, Fr & De

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Book Description :

Download Approximation Theory in Tensor Product Spaces book written by William A. Light,Elliot W. Cheney, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Functional Equations Inequalities and Applications

Functional Equations  Inequalities and Applications Book
Author : Themistocles M. Rassias
Publisher : Springer Science & Business Media
Release : 2003-09-30
ISBN : 9781402015786
Language : En, Es, Fr & De

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Book Description :

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

Duality in Analytic Number Theory

Duality in Analytic Number Theory Book
Author : Peter D. T. A. Elliott
Publisher : Cambridge University Press
Release : 1997-02-13
ISBN : 1316582590
Language : En, Es, Fr & De

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Book Description :

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.

Number Theory

Number Theory Book
Author : R.P. Bambah,V.C. Dumir,R.J. Hans-Gill
Publisher : Birkhäuser
Release : 2012-12-06
ISBN : 303487023X
Language : En, Es, Fr & De

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Book Description :

The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.

Multivariate Approximation Theory

Multivariate Approximation Theory Book
Author : E. W. Cheney
Publisher : SIAM
Release : 1986-01-01
ISBN : 9781611970197
Language : En, Es, Fr & De

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Book Description :

The approximation of functions of several variables continues to be a difficult problem in scientific computing because many of the algorithms required for such problems have yet to be written. This monograph is written for a broad audience of computational mathematicians and statisticians concerned with the development of algorithms or the derivation of approximations from linear projections, of which the interpolating operators are an important example. As an aid to both researchers and students, a bibliography of more than 200 titles is included.

Analytic Number Theory

Analytic Number Theory Book
Author : Japan) Taniguchi International Symposium on Mathematics: Analytic Number Theory (1996 : Kyoto
Publisher : Cambridge University Press
Release : 1997-10-16
ISBN : 0521625122
Language : En, Es, Fr & De

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Book Description :

Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.

The Theory of the Riemann Zeta function

The Theory of the Riemann Zeta function Book
Author : Late Savilian Professor of Geometry E C Titchmarsh,Edward Charles Titchmarsh,Titchmarsh,D. R. Heath-Brown,Titchmarsh, Edward Charles Titchmarsh
Publisher : Oxford University Press
Release : 1986
ISBN : 9780198533696
Language : En, Es, Fr & De

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Book Description :

The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.

Notes from the International Autumn School on Computational Number Theory

Notes from the International Autumn School on Computational Number Theory Book
Author : Ilker Inam,Engin Büyükaşık
Publisher : Springer
Release : 2019-04-17
ISBN : 3030125580
Language : En, Es, Fr & De

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Book Description :

This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include: Modular forms L-functions The modular symbols algorithm Diophantine equations Nullstellensatz Eisenstein series Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field as well.

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

Functional Equations Results and Advances

Functional Equations     Results and Advances Book
Author : Zoltan Daroczy,Zsolt Páles
Publisher : Springer Science & Business Media
Release : 2013-06-29
ISBN : 1475752881
Language : En, Es, Fr & De

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Book Description :

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. First of all, this is due to the fact that the mathematical applications raised the investigations of newer and newer types of functional equations. At the same time, the self development of this theory was also very fruitful. This can be followed in many monographs that treat and discuss the various methods and approaches. These developments were also essentially influenced by a number jour nals, for instance, by the Publicationes Mathematicae Debrecen (founded in 1953) and by the Aequationes Mathematicae (founded in 1968), be cause these journals published papers from the field of functional equa tions readily and frequently. The latter journal also publishes the yearly report of the International Symposia on Functional Equations and a comprehensive bibliography of the most recent papers. At the same time, there are periodically and traditionally organized conferences in Poland and in Hungary devoted to functional equations and inequali ties. In 2000, the 38th International Symposium on Functional Equations was organized by the Institute of Mathematics and Informatics of the University of Debrecen in Noszvaj, Hungary. The report about this meeting can be found in Aequationes Math. 61 (2001), 281-320.

Analytic Number Theory Mathematical Analysis and Their Applications

Analytic Number Theory  Mathematical Analysis and Their Applications Book
Author : Nikolaĭ Nikolaevich Bogoli︠u︡bov,K. K. Mardzhanishvili
Publisher : American Mathematical Soc.
Release : 1984
ISBN : 9780821830772
Language : En, Es, Fr & De

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Book Description :

This ""Proceedings of the Steklov Institute of Mathematics"" together with the volume preceding it (Volume 157), is a collection of papers dedicated to Academician I. M. Vinogradov on his ninetieth birthday. This volume contains original papers on various branches of mathematics: analytic number theory, algebra, partial differential equations, probability theory, and differential games.