Mean Value Theorems And Functional Equations PDF Download
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Author: Thomas Riedel
Publisher: World Scientific
ISBN: 9814495875
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.
Author: Thomas Riedel
Publisher: World Scientific
ISBN: 9814495875
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.
Author: Prasanna Sahoo
Publisher: World Scientific
ISBN: 9789810235444
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.
Author: Themistocles RASSIAS
Publisher: Springer Science & Business Media
ISBN: 940170225X
Category : Mathematics
Languages : en
Pages : 221
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Book Description
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.
Author: B. Forte
Publisher: Springer Science & Business Media
ISBN: 3642110045
Category : Mathematics
Languages : en
Pages : 433
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Book Description
J. Aczél: Some applications of functional equations and inequalities to information measures.- J.A. Baker: Functional equations in vector space, part II.- I Fenyo: Sur les équations distributionnelles.- B. Forte: Applications of functional equations and inequalities to information theory.- S. Golab: Sur l’équation fonctionnelle des brigade.- E. Hille: Mean-values and functional equations.- J. Kampé de Feriet: Applications of functional equations and inequalities to information theory. Measure of information by a set of observers: a functional equation.- M. Kuczma: Convex functions.- S. Kurepa: Functional equations on vector spaces.- E. Lukacs: Inequalities and functional equations in probability theory.- M.A. McKiernan: Difference and mean-value type functional equations.- T.S. Motzkin: Solutions of differential and functional inequalities.- C.T. Ng: Uniqueness theorems in the theory of functional equations and related homotopy.- A.M. Ostrowski: Integral inequalities.- H. Schwerdtfeger: Remark on an inequality for monotonic functions.
Author: Prasanna K. Sahoo
Publisher: CRC Press
ISBN: 1439841160
Category : Mathematics
Languages : en
Pages : 465
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Book Description
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 p
Author: Yeol Je Cho
Publisher: Springer Science & Business Media
ISBN: 1461484774
Category : Mathematics
Languages : en
Pages : 255
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Book Description
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.
Author: Edgar W. Kaucher
Publisher: Elsevier
ISBN: 1483273776
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic. After a brief overview of the different self-validating approaches, this book goes on introducing the mathematical preliminaries consisting principally of fixed-point theorems and the computational context for the development of validating methods in function spaces. The subsequent chapters deals with the development and application of point of view of ultra-arithmetic and the constructs of function-space arithmetic spaces, such as spaces, bases, rounding, and approximate operations. These topics are followed by discussion of the iterative residual correction methods for function problems and the requirements of a programming language needed to make the tools and constructs of the methodology available in actual practice on a computer. The last chapter describes the techniques for adapting the methodologies to a computer, including the self-validating results for specific problems. This book will prove useful to mathematicians and advance mathematics students.
Author: Palaniappan Kannappan
Publisher: Springer Science & Business Media
ISBN: 0387894926
Category : Mathematics
Languages : en
Pages : 817
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Book Description
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.
Author: Abdul Kadir Aziz
Publisher:
ISBN:
Category : Differential calculus
Languages : en
Pages : 38
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Book Description
In a recent paper the writers obtained a mean value theorem for vector valued functions of a real variable which plays a role analogous to that of Lagrange's mean value theorem in the differential calculus of real valued functions. This report contains an analysis of various methods for proving these theorems.
Author: Asen L. Dontchev
Publisher: Springer
ISBN: 149391037X
Category : Mathematics
Languages : en
Pages : 495
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Book Description
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.
