Theory of Approximate Functional Equations Book

Theory of Approximate Functional Equations


  • Author : Madjid Eshaghi Gordji
  • Publisher : Academic Press
  • Release Date : 2016-03-03
  • Genre: Mathematics
  • Pages : 148
  • ISBN 10 : 9780128039717

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Theory of Approximate Functional Equations Excerpt :

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 Book

Handbook of Functional Equations


  • Author : Themistocles M. Rassias
  • Publisher : Springer
  • Release Date : 2014-11-21
  • Genre: Mathematics
  • Pages : 396
  • ISBN 10 : 9781493912865

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Handbook of Functional Equations Excerpt :

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.

Introduction to Functional Equations Book
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Introduction to Functional Equations


  • Author : Costas Efthimiou
  • Publisher : American Mathematical Soc.
  • Release Date : 2011-10-13
  • Genre: Mathematics
  • Pages : 363
  • ISBN 10 : 9780821853146

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Introduction to Functional Equations Excerpt :

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 Book

Optimal Control of Differential and Functional Equations


  • Author : J. Warga
  • Publisher : Academic Press
  • Release Date : 2014-05-10
  • Genre: Technology & Engineering
  • Pages : 546
  • ISBN 10 : 9781483259192

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Optimal Control of Differential and Functional Equations Excerpt :

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 Book

The Riemann Zeta Function


  • Author : Aleksandar Ivic
  • Publisher : Courier Corporation
  • Release Date : 2012-07-12
  • Genre: Mathematics
  • Pages : 562
  • ISBN 10 : 9780486140049

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The Riemann Zeta Function Excerpt :

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 Analysis  Approximation Theory  and Numerical Analysis Book

Functional Analysis Approximation Theory and Numerical Analysis


  • Author : John Michael Rassias
  • Publisher : World Scientific
  • Release Date : 1994
  • Genre: Mathematics
  • Pages : 342
  • ISBN 10 : 9810207379

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Functional Analysis Approximation Theory and Numerical Analysis Excerpt :

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.

Stability of Functional Equations in Several Variables Book

Stability of Functional Equations in Several Variables


  • Author : D.H. Hyers
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 318
  • ISBN 10 : 9781461217909

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Stability of Functional Equations in Several Variables Excerpt :

The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the pre sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equa tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved co author and friend Professor Donald H. Hyers passed away.

Duality in Analytic Number Theory Book

Duality in Analytic Number Theory


  • Author : Peter D. T. A. Elliott
  • Publisher : Cambridge University Press
  • Release Date : 1997-02-13
  • Genre: Mathematics
  • Pages : null
  • ISBN 10 : 9781316582596

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Duality in Analytic Number Theory Excerpt :

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.

Functional Equations  History  Applications and Theory Book

Functional Equations History Applications and Theory


  • Author : J. Aczél
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 246
  • ISBN 10 : 9789400963207

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Functional Equations History Applications and Theory Excerpt :

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.

Analytic Number Theory Book

Analytic Number Theory


  • Author : Yoichi Motohashi
  • Publisher : Cambridge University Press
  • Release Date : 1997-10-16
  • Genre: Mathematics
  • Pages : 396
  • ISBN 10 : 9780521625128

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Analytic Number Theory Excerpt :

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

The Theory of the Riemann Zeta function Book
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The Theory of the Riemann Zeta function


  • Author : Late Savilian Professor of Geometry E C Titchmarsh
  • Publisher : Oxford University Press
  • Release Date : 1986
  • Genre: Architecture
  • Pages : 428
  • ISBN 10 : 0198533691

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The Theory of the Riemann Zeta function Excerpt :

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

Functional Equations  Inequalities and Applications Book

Functional Equations Inequalities and Applications


  • Author : Themistocles M. Rassias
  • Publisher : Springer Science & Business Media
  • Release Date : 2003-09-30
  • Genre: Mathematics
  • Pages : 244
  • ISBN 10 : 140201578X

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Functional Equations Inequalities and Applications Excerpt :

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.

Notes from the International Autumn School on Computational Number Theory Book

Notes from the International Autumn School on Computational Number Theory


  • Author : Ilker Inam
  • Publisher : Springer
  • Release Date : 2019-04-17
  • Genre: Mathematics
  • Pages : 363
  • ISBN 10 : 9783030125585

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Notes from the International Autumn School on Computational Number Theory Excerpt :

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.

Functional Equations     Results and Advances Book

Functional Equations Results and Advances


  • Author : Zoltan Daroczy
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Mathematics
  • Pages : 361
  • ISBN 10 : 9781475752885

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Functional Equations Results and Advances Excerpt :

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.

Applied Functional Analysis  Approximation Methods and Computers Book

Applied Functional Analysis Approximation Methods and Computers


  • Author : S.S. Kutateladze
  • Publisher : CRC Press
  • Release Date : 2010-12-12
  • Genre: Mathematics
  • Pages : 400
  • ISBN 10 : 1420050125

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Applied Functional Analysis Approximation Methods and Computers Excerpt :

This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.