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Theory of Approximate Functional Equations

Theory of Approximate Functional Equations
In Banach Algebras, Inner Product Spaces and Amenable Groups

by Madjid Eshaghi Gordji,Sadegh Abbaszadeh

  • Publisher : Academic Press
  • Release : 2016-03-03
  • Pages : 148
  • ISBN : 012803971X
  • Language : En, Es, Fr & De
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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
Stability Theory

by Themistocles M. Rassias

  • Publisher : Springer
  • Release : 2014-11-21
  • Pages : 396
  • ISBN : 1493912860
  • Language : En, Es, Fr & De
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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 Analysis, Approximation Theory and Numerical Analysis

Functional Analysis, Approximation Theory and Numerical Analysis
A Book

by John M Rassias

  • Publisher : World Scientific
  • Release : 1994-06-09
  • Pages : 340
  • ISBN : 9814506052
  • Language : En, Es, Fr & De
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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

Iterative Functional Equations

Iterative Functional Equations
A Book

by Marek Kuczma,Bogdan Choczewski,Roman Ger

  • Publisher : Cambridge University Press
  • Release : 1990-07-27
  • Pages : 552
  • ISBN : 9780521355612
  • Language : En, Es, Fr & De
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A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.

The Riemann Zeta-Function

The Riemann Zeta-Function
Theory and Applications

by Aleksandar Ivic

  • Publisher : Courier Corporation
  • Release : 2012-07-12
  • Pages : 562
  • ISBN : 0486140040
  • Language : En, Es, Fr & De
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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.

An Introduction to the Theory of the Riemann Zeta-Function

An Introduction to the Theory of the Riemann Zeta-Function
A Book

by S. J. Patterson

  • Publisher : Cambridge University Press
  • Release : 1995-02-02
  • Pages : 329
  • ISBN : 131658335X
  • Language : En, Es, Fr & De
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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.

Developments in Functional Equations and Related Topics

Developments in Functional Equations and Related Topics
A Book

by Anonim

  • Publisher : Springer
  • Release : 2017
  • Pages : 329
  • ISBN : 331961732X
  • Language : En, Es, Fr & De
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Functional Equations, Inequalities and Applications

Functional Equations, Inequalities and Applications
A Book

by Themistocles M. Rassias

  • Publisher : Springer Science & Business Media
  • Release : 2003-09-30
  • Pages : 224
  • ISBN : 9781402015786
  • Language : En, Es, Fr & De
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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
A Book

by Peter D. T. A. Elliott

  • Publisher : Cambridge University Press
  • Release : 1997-02-13
  • Pages : 329
  • ISBN : 1316582590
  • Language : En, Es, Fr & De
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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.

Frontiers in Functional Equations and Analytic Inequalities

Frontiers in Functional Equations and Analytic Inequalities
A Book

by George A. Anastassiou,John Michael Rassias

  • Publisher : Springer Nature
  • Release : 2019-11-23
  • Pages : 753
  • ISBN : 3030289508
  • Language : En, Es, Fr & De
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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.

Analytic Number Theory

Analytic Number Theory
A Book

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

  • Publisher : Cambridge University Press
  • Release : 1997-10-16
  • Pages : 382
  • ISBN : 9780521625128
  • Language : En, Es, Fr & De
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Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.

The Riemann Zeta-Function

The Riemann Zeta-Function
A Book

by Anatoly A. Karatsuba,S. M. Voronin

  • Publisher : Walter de Gruyter
  • Release : 1992-01-01
  • Pages : 408
  • ISBN : 3110886146
  • Language : En, Es, Fr & De
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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Itinerant Seminar on Functional Equations, Approximation and Convexity

Itinerant Seminar on Functional Equations, Approximation and Convexity
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1990
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Topics in Mathematical Analysis and Applications

Topics in Mathematical Analysis and Applications
A Book

by Themistocles M. Rassias,László Tóth

  • Publisher : Springer
  • Release : 2014-10-13
  • Pages : 814
  • ISBN : 3319065548
  • Language : En, Es, Fr & De
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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.

The Theory of Hardy's Z-Function

The Theory of Hardy's Z-Function
A Book

by A. Ivić

  • Publisher : Cambridge University Press
  • Release : 2013
  • Pages : 245
  • ISBN : 1107028833
  • Language : En, Es, Fr & De
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"This book is an outgrowth of a mini-course held at the Arctic Number Theory School, University of Helsinki, May 18-25, 2011. The central topic is Hardy's function, of great importance in the theory of the Riemann zeta-function. It is named after GodfreyHarold Hardy FRS (1877-1947), who was a prominent English mathematician, well-known for his achievements in number theory and mathematical analysis"--

Applications of Nonlinear Analysis

Applications of Nonlinear Analysis
A Book

by Themistocles M. Rassias

  • Publisher : Springer
  • Release : 2018-06-29
  • Pages : 931
  • ISBN : 3319898159
  • Language : En, Es, Fr & De
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New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.

The Lerch zeta-function

The Lerch zeta-function
A Book

by Antanas Laurinčikas,Antanas Laurincikas,Ramunas Garunkstis,Ramūnas Garunkštis

  • Publisher : Springer Science & Business Media
  • Release : 2002
  • Pages : 189
  • ISBN : 9781402010149
  • Language : En, Es, Fr & De
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This monograph is a generalization of the classic Riemann, and Hurwitz zeta-functions, containing both analytic and probability theory of Lerch zeta-functions.

Reviews in Number Theory, 1984-96

Reviews in Number Theory, 1984-96
As Printed in Mathematical Reviews

by Anonim

  • Publisher : Amer Mathematical Society
  • Release : 1997
  • Pages : 1012
  • ISBN : 9780821809372
  • Language : En, Es, Fr & De
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These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

Computational Mathematics and Variational Analysis

Computational Mathematics and Variational Analysis
A Book

by Nicholas J. Daras,Themistocles M. Rassias

  • Publisher : Springer Nature
  • Release : 2020-06-06
  • Pages : 568
  • ISBN : 3030446255
  • Language : En, Es, Fr & De
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This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.

Ulam Type Stability

Ulam Type Stability
A Book

by Janusz Brzdęk,Dorian Popa,Themistocles M. Rassias

  • Publisher : Springer Nature
  • Release : 2019-10-29
  • Pages : 514
  • ISBN : 3030289729
  • Language : En, Es, Fr & De
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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.