Functional Equations Results And Advances

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Functional Equations — Results and Advances

Author : Zoltan Daroczy
Publisher : Springer Science & Business Media
ISBN 13 : 1475752881
Total Pages : 359 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Functional Equations — Results and Advances by : Zoltan Daroczy

Download or read book Functional Equations — Results and Advances written by Zoltan Daroczy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 359 pages. Available in PDF, EPUB and Kindle. Book 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.

Developments in Functional Equations and Related Topics

Author : Janusz Brzdęk
Publisher : Springer
ISBN 13 : 331961732X
Total Pages : 354 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Developments in Functional Equations and Related Topics by : Janusz Brzdęk

Download or read book Developments in Functional Equations and Related Topics written by Janusz Brzdęk and published by Springer. This book was released on 2017-08-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Differential Equations

Author : Constantin Corduneanu
Publisher : John Wiley & Sons
ISBN 13 : 1119189470
Total Pages : 362 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Functional Differential Equations by : Constantin Corduneanu

Download or read book Functional Differential Equations written by Constantin Corduneanu and published by John Wiley & Sons. This book was released on 2016-04-11 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.

Regularity Properties of Functional Equations in Several Variables

Author : Antal Járai
Publisher : Springer Science & Business Media
ISBN 13 : 038724414X
Total Pages : 367 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Regularity Properties of Functional Equations in Several Variables by : Antal Járai

Download or read book Regularity Properties of Functional Equations in Several Variables written by Antal Járai and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.

Stability of Functional Equations in Several Variables

Author : D.H. Hyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461217903
Total Pages : 323 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stability of Functional Equations in Several Variables by : D.H. Hyers

Download or read book Stability of Functional Equations in Several Variables written by D.H. Hyers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book 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.

Functional Equations on Groups

Author : Henrik Stetkr
Publisher : World Scientific
ISBN 13 : 981451313X
Total Pages : 395 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Functional Equations on Groups by : Henrik Stetkr

Download or read book Functional Equations on Groups written by Henrik Stetkr and published by World Scientific. This book was released on 2013 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Functional Equations

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 1493912860
Total Pages : 394 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Handbook of Functional Equations by : Themistocles M. Rassias

Download or read book Handbook of Functional Equations written by Themistocles M. Rassias and published by Springer. This book was released on 2014-11-21 with total page 394 pages. Available in PDF, EPUB and Kindle. Book 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.

Stability of Some Advanced Functional Equations in Various Spaces

Author : Hemen Dutta
Publisher : Springer Nature
ISBN 13 : 3031337042
Total Pages : 260 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Stability of Some Advanced Functional Equations in Various Spaces by : Hemen Dutta

Download or read book Stability of Some Advanced Functional Equations in Various Spaces written by Hemen Dutta and published by Springer Nature. This book was released on 2023-08-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to present several new results concerning solution and various stabilities of some functional equations in various spaces. The chapters consider various spaces to investigate stabilities justifying that stability results hold well in those spaces. It also includes results proving new insight to analyze approximate solutions to a given equation whenever uncertainty occurs. The presentation of the book should be useful for graduated students and researchers interested in the theory of functional equations to understand the useful ideas involved and problems to study further.

Combinatorial Functional Equations

Author : Yanpei Liu
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110627337
Total Pages : 372 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Combinatorial Functional Equations by : Yanpei Liu

Download or read book Combinatorial Functional Equations written by Yanpei Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-12-16 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The second volume mainly presents several kinds of meson functional equations which are divided into three types: outer, inner and surface. It is suited for a wide readership, including pure and applied mathematicians, and also computer scientists.

Functional Equations in Several Variables

Author : J. Aczél
Publisher : Cambridge University Press
ISBN 13 : 9780521352765
Total Pages : 490 pages
Book Rating : 4.3/5 (527 download)

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Book Synopsis Functional Equations in Several Variables by : J. Aczél

Download or read book Functional Equations in Several Variables written by J. Aczél and published by Cambridge University Press. This book was released on 1989 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum.

Introduction to Functional Equations

Author : Prasanna K. Sahoo
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781439841112
Total Pages : 0 pages
Book Rating : 4.8/5 (411 download)

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Book Synopsis Introduction to Functional Equations by : Prasanna K. Sahoo

Download or read book Introduction to Functional Equations written by Prasanna K. Sahoo and published by Chapman and Hall/CRC. This book was released on 2011-02-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Advances in Integral Equations

Author : Francisco Bulnes
Publisher : BoD – Books on Demand
ISBN 13 : 183880658X
Total Pages : 102 pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Recent Advances in Integral Equations by : Francisco Bulnes

Download or read book Recent Advances in Integral Equations written by Francisco Bulnes and published by BoD – Books on Demand. This book was released on 2019-07-24 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral equations are functional equations in which an unknown function appears under an integral sign. This can involve aspects of function theory and their integral transforms when the unknown function appears with a functional non-degenerated kernel under the integral sign. The close relation between differential and integral equations does that in some functional analysis, and function theory problems may be formulated either way. This book establishes the fundamentals of integral equations and considers some deep research aspects on integral equations of first and second kind, operator theory applied to integral equations, methods to solve some nonlinear integral equations, and singular integral equations, among other things. This is the first volume on this theme, hoping that other volumes of this important functional analysis theme and operator theory to formal functional equations will be realized in the future.

Iterative Functional Equations

Author : Marek Kuczma
Publisher : Cambridge University Press
ISBN 13 : 9780521355612
Total Pages : 580 pages
Book Rating : 4.3/5 (556 download)

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Book Synopsis Iterative Functional Equations by : Marek Kuczma

Download or read book Iterative Functional Equations written by Marek Kuczma and published by Cambridge University Press. This book was released on 1990-07-27 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Equations And Inequalities: Solutions And Stability Results

Author : John Michael Rassias
Publisher : World Scientific Publishing Company
ISBN 13 : 9813147628
Total Pages : 397 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Functional Equations And Inequalities: Solutions And Stability Results by : John Michael Rassias

Download or read book Functional Equations And Inequalities: Solutions And Stability Results written by John Michael Rassias and published by World Scientific Publishing Company. This book was released on 2017-03-20 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.

On Applications and Theory of Functional Equations

Author : J. Aczél
Publisher : Academic Press
ISBN 13 : 1483262650
Total Pages : 65 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis On Applications and Theory of Functional Equations by : J. Aczél

Download or read book On Applications and Theory of Functional Equations written by J. Aczél and published by Academic Press. This book was released on 2014-05-12 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Applications and Theory of Functional Equations focuses on the principles and advancement of numerical approaches used in functional equations. The publication first offers information on the history of functional equations, noting that the research on functional equations originated in problems related to applied mathematics. The text also highlights the influence of J. d'Alembert, S. D. Poisson, E. Picard, and A. L. Cauchy in promoting the processes of numerical analyses involving functional equations. The role of vectors in solving functional equations is also noted. The book ponders on the international Fifth Annual Meeting on Functional Equations, held in Waterloo, Ontario, Canada on April 24-30, 1967. The meeting gathered participants from America, Asia, Australia, and Europe. One of the topics presented at the meeting focuses on the survey of materials dealing with the progress of approaches in the processes and methodologies involved in solving problems dealing with functional equations. The influence, works, and contributions of A. L. Cauchy, G. Darboux, and G. S. Young to the field are also underscored. The publication is a valuable reference for readers interested in functional equations.

One-dimensional Functional Equations

Author : Genrich Belitskii
Publisher : Birkhäuser
ISBN 13 : 3034880790
Total Pages : 223 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis One-dimensional Functional Equations by : Genrich Belitskii

Download or read book One-dimensional Functional Equations written by Genrich Belitskii and published by Birkhäuser. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle. Such equations systematically arise in dynamical systems, differential equations, probabilities, singularities of smooth mappings, and other areas. The purpose of the book is to present modern methods and new results in the subject, with an emphasis on a connection between local and global solvability. The general concepts developed in the book are applicable to multidimensional functional equations. Some of the methods are presented for the first time in the monograph literature. The book is addressed to graduates and researchers interested in dynamical systems, differential equations, operator theory, or the theory of functions and their applications.

Handbook of Functional Equations

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 1493912461
Total Pages : 555 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Handbook of Functional Equations by : Themistocles M. Rassias

Download or read book Handbook of Functional Equations written by Themistocles M. Rassias and published by Springer. This book was released on 2014-11-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.