# Theory Of Approximate Functional Equations

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## Theory of Approximate Functional Equations

Author | : Madjid Eshaghi Gordji,Sadegh Abbaszadeh |

Publsiher | : Academic Press |

Total Pages | : 148 |

Release | : 2016-03-03 |

ISBN 10 | : 012803971X |

ISBN 13 | : 9780128039717 |

Language | : EN, FR, DE, ES & NL |

**Theory of Approximate Functional Equations Book Review:**

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

## Introduction to Functional Equations

Author | : Costas Efthimiou |

Publsiher | : American Mathematical Soc. |

Total Pages | : 363 |

Release | : 2011-10-13 |

ISBN 10 | : 0821853147 |

ISBN 13 | : 9780821853146 |

Language | : EN, FR, DE, ES & NL |

**Introduction to Functional Equations Book Review:**

Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

## Optimal Control of Differential and Functional Equations

Author | : J. Warga |

Publsiher | : Academic Press |

Total Pages | : 546 |

Release | : 2014-05-10 |

ISBN 10 | : 1483259196 |

ISBN 13 | : 9781483259192 |

Language | : EN, FR, DE, ES & NL |

**Optimal Control of Differential and Functional Equations Book Review:**

Optimal Control of Differential and Functional Equations presents a mathematical theory of deterministic optimal control, with emphasis on problems involving functional-integral equations and functional restrictions. The book reviews analytical foundations, and discusses deterministic optimal control problems requiring original, approximate, or relaxed solutions. Original solutions involve mathematicians, and approximate solutions concern engineers. Relaxed solutions yield a complete theory that encompasses both existence theorems and necessary conditions. The text also presents general optimal control problems, optimal control of ordinary differential equations, and different types of functional-integral equations. The book discusses control problems defined by equations in Banach spaces, the convex cost functionals, and the weak necessary conditions for an original minimum. The text illustrates a class of ordinary differential problems with examples, and explains some conflicting control problems with relaxed adverse controls, as well as conflicting control problems with hyper-relaxed adverse controls. The book is intended for mature mathematicians, graduate students in analysis, and practitioners of optimal control whose primary interests and training are in science or engineering.

## The Riemann Zeta Function

Author | : Aleksandar Ivic |

Publsiher | : Courier Corporation |

Total Pages | : 562 |

Release | : 2012-07-12 |

ISBN 10 | : 0486140040 |

ISBN 13 | : 9780486140049 |

Language | : EN, FR, DE, ES & NL |

**The Riemann Zeta Function Book Review:**

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.

## Functional Equations History Applications and Theory

Author | : J. Aczél |

Publsiher | : Springer Science & Business Media |

Total Pages | : 246 |

Release | : 2001-11-30 |

ISBN 10 | : 9781402003295 |

ISBN 13 | : 1402003293 |

Language | : EN, FR, DE, ES & NL |

**Functional Equations History Applications and Theory Book Review:**

Approach your problems from It isn't that they can't see the right end and begin with the solution. It is that they the answers. Then one day, can't see the problem. perhaps you will find the G.K. Chesterton. The Scandal of final question. Father Brown 'The Point of a Pin' . 'The Hermit Clad ~n Crane Feathers' in R. van Gulik's The Chinese Haze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathe matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) ~n re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are rele vant to filtering; and prediction and electrical en~ineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existinf, classifi~ation schemes. They draw upon widely different sections of mathematics.

## Approximation Theory in Tensor Product Spaces

Author | : William A. Light,Elliot W. Cheney |

Publsiher | : Springer |

Total Pages | : 158 |

Release | : 2006-11-14 |

ISBN 10 | : 3540397418 |

ISBN 13 | : 9783540397410 |

Language | : EN, FR, DE, ES & NL |

**Approximation Theory in Tensor Product Spaces Book Review:**

## The Lerch zeta function

Author | : Antanas Laurincikas,Ramunas Garunkstis |

Publsiher | : Springer Science & Business Media |

Total Pages | : 189 |

Release | : 2013-12-11 |

ISBN 10 | : 9401764018 |

ISBN 13 | : 9789401764018 |

Language | : EN, FR, DE, ES & NL |

**The Lerch zeta function Book Review:**

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.

## Duality in Analytic Number Theory

Author | : Peter D. T. A. Elliott |

Publsiher | : Cambridge University Press |

Total Pages | : 135 |

Release | : 1997-02-13 |

ISBN 10 | : 1316582590 |

ISBN 13 | : 9781316582596 |

Language | : EN, FR, DE, ES & NL |

**Duality in Analytic Number Theory Book Review:**

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.

## Handbook of Functional Equations

Author | : Themistocles M. Rassias |

Publsiher | : Springer |

Total Pages | : 396 |

Release | : 2014-11-21 |

ISBN 10 | : 1493912860 |

ISBN 13 | : 9781493912865 |

Language | : EN, FR, DE, ES & NL |

**Handbook of Functional Equations Book Review:**

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.

## Functional Equations Inequalities and Applications

Author | : Themistocles RASSIAS |

Publsiher | : Springer Science & Business Media |

Total Pages | : 224 |

Release | : 2013-03-09 |

ISBN 10 | : 940170225X |

ISBN 13 | : 9789401702256 |

Language | : EN, FR, DE, ES & NL |

**Functional Equations Inequalities and Applications Book Review:**

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.

## Functional Analysis Approximation Theory and Numerical Analysis

Author | : John Michael Rassias |

Publsiher | : World Scientific |

Total Pages | : 325 |

Release | : 1994 |

ISBN 10 | : 9789810207373 |

ISBN 13 | : 9810207379 |

Language | : EN, FR, DE, ES & NL |

**Functional Analysis Approximation Theory and Numerical Analysis Book Review:**

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.

## Analytic Number Theory

Author | : Japan) Taniguchi International Symposium on Mathematics: Analytic Number Theory (1996 : Kyoto |

Publsiher | : Cambridge University Press |

Total Pages | : 382 |

Release | : 1997-10-16 |

ISBN 10 | : 0521625122 |

ISBN 13 | : 9780521625128 |

Language | : EN, FR, DE, ES & NL |

**Analytic Number Theory Book Review:**

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

## Developments in Functional Equations and Related Topics

Author | : Janusz Brzdęk,Krzysztof Ciepliński,Themistocles M. Rassias |

Publsiher | : Springer |

Total Pages | : 352 |

Release | : 2017-08-14 |

ISBN 10 | : 331961732X |

ISBN 13 | : 9783319617329 |

Language | : EN, FR, DE, ES & NL |

**Developments in Functional Equations and Related Topics Book Review:**

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.

## The Theory of the Riemann Zeta function

Author | : Late Savilian Professor of Geometry E C Titchmarsh,Edward Charles Titchmarsh,Titchmarsh,D. R. Heath-Brown,Titchmarsh, Edward Charles Titchmarsh |

Publsiher | : Oxford University Press |

Total Pages | : 412 |

Release | : 1986 |

ISBN 10 | : 9780198533696 |

ISBN 13 | : 0198533691 |

Language | : EN, FR, DE, ES & NL |

**The Theory of the Riemann Zeta function Book Review:**

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

Author | : Ilker Inam,Engin Büyükaşık |

Publsiher | : Springer |

Total Pages | : 363 |

Release | : 2019-04-17 |

ISBN 10 | : 3030125580 |

ISBN 13 | : 9783030125585 |

Language | : EN, FR, DE, ES & NL |

**Notes from the International Autumn School on Computational Number Theory Book Review:**

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.

## Stability of Functional Equations in Random Normed Spaces

Author | : Yeol Je Cho,Themistocles M. Rassias,Reza Saadati |

Publsiher | : Springer Science & Business Media |

Total Pages | : 246 |

Release | : 2013-08-27 |

ISBN 10 | : 1461484774 |

ISBN 13 | : 9781461484776 |

Language | : EN, FR, DE, ES & NL |

**Stability of Functional Equations in Random Normed Spaces Book Review:**

This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.

## Topics in Recent Zeta Function Theory

Author | : A. Ivić |

Publsiher | : Unknown |

Total Pages | : 272 |

Release | : 1983 |

ISBN 10 | : 1928374650XXX |

ISBN 13 | : UOM:39015015698593 |

Language | : EN, FR, DE, ES & NL |

**Topics in Recent Zeta Function Theory Book Review:**

## Analytic Number Theory Mathematical Analysis and Their Applications

Author | : Nikolaĭ Nikolaevich Bogoli︠u︡bov,K. K. Mardzhanishvili |

Publsiher | : American Mathematical Soc. |

Total Pages | : 247 |

Release | : 1984 |

ISBN 10 | : 9780821830772 |

ISBN 13 | : 0821830775 |

Language | : EN, FR, DE, ES & NL |

**Analytic Number Theory Mathematical Analysis and Their Applications Book Review:**

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.

## Best Approximation by Linear Superpositions approximate Nomography

Author | : S. I͡A. Khavinson |

Publsiher | : American Mathematical Soc. |

Total Pages | : 175 |

Release | : 1997-01-01 |

ISBN 10 | : 9780821897737 |

ISBN 13 | : 082189773X |

Language | : EN, FR, DE, ES & NL |

**Best Approximation by Linear Superpositions approximate Nomography Book Review:**

This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions D considered as a sub-space of the space of continous functions C(X) on a compact space X. Such properties as density of D in C(X), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.

## Proceedings of the International Conference on Number Theory Moscow September 14 18 1971

Author | : Ivan Matveevich Vinogradov |

Publsiher | : American Mathematical Soc. |

Total Pages | : 298 |

Release | : 1975 |

ISBN 10 | : 9780821830321 |

ISBN 13 | : 0821830325 |

Language | : EN, FR, DE, ES & NL |

**Proceedings of the International Conference on Number Theory Moscow September 14 18 1971 Book Review:**

Papers and articles about number theory.