Functional Equations On Groups
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Functional Equations On Groups
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Author : Henrik Stetkaer
language : en
Publisher: World Scientific
Release Date : 2013-07-15
Functional Equations On Groups written by Henrik Stetkaer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-15 with Mathematics categories.
This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, ℝ). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.
Functional Equations On Groups
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Author : Henrik Stetkr
language : en
Publisher: World Scientific
Release Date : 2013
Functional Equations On Groups written by Henrik Stetkr and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, R). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.
Functional Equations And Inequalities With Applications
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Author : Palaniappan Kannappan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-10
Functional Equations And Inequalities With Applications written by Palaniappan Kannappan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-10 with Mathematics categories.
Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.
Introduction To Functional Equations
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Author : Prasanna K. Sahoo
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2011-02-08
Introduction To Functional Equations written by Prasanna K. Sahoo and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-08 with Mathematics categories.
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections highlighting various developments of the main equations treated in that chapter. For advanced students, the book introduces functional equations in abstract domains like semigroups, groups, and Banach spaces. Functional equations covered include: Cauchy Functional Equations and Applications The Jensen Functional Equation Pexider's Functional Equation Quadratic Functional Equation D'Alembert Functional Equation Trigonometric Functional Equations Pompeiu Functional Equation Hosszu Functional Equation Davison Functional Equation Abel Functional Equation Mean Value Type Functional Equations Functional Equations for Distance Measures The innovation of solving functional equations lies in finding the right tricks for a particular equation. Accessible and rooted in current theory, methods, and research, this book sharpens mathematical competency and prepares students of mathematics and engineering for further work in advanced functional equations.
Handbook Of Functional Equations
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-11-21
Handbook Of Functional Equations written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.
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.
Convolution Type Functional Equations On Topological Abelian Groups
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Author : L szl¢ Szkelyhidi
language : en
Publisher: World Scientific
Release Date : 1991
Convolution Type Functional Equations On Topological Abelian Groups written by L szl¢ Szkelyhidi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results.
Functional Equations And Characterization Problems On Locally Compact Abelian Groups
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Author : Gennadiĭ Mikhaĭlovich Felʹdman
language : en
Publisher: European Mathematical Society
Release Date : 2008
Functional Equations And Characterization Problems On Locally Compact Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Abelian groups categories.
This book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group $X$. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac-Bernstein, Skitovich-Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of $X$. Group analogs of the Cramer and Marcinkiewicz theorems are also studied. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory.
Frontiers In Functional Equations And Analytic Inequalities
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2019-11-23
Frontiers In Functional Equations And Analytic Inequalities written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-23 with Mathematics categories.
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.
The Theory Of Finite Groups
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Author : Hans Kurzweil
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-06
The Theory Of Finite Groups written by Hans Kurzweil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-06 with Mathematics categories.
From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews
Introduction To Functional Equations
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Author : Costas Efthimiou
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-10-13
Introduction To Functional Equations written by Costas Efthimiou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
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.