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Author : Joachim Domsta
Publisher :
ISBN 13 : 9788373260627
Total Pages : 161 pages
Book Rating : 4.2/5 (66 download)
Download or read book Regularly Varying Solutions of Linear Functional Equations in a Single Variable written by Joachim Domsta and published by . This book was released on 2002 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marek Kuczma
Publisher :
ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.:/5 (89 download)
Download or read book Functional Equations in a Single Variable written by Marek Kuczma and published by . This book was released on 1968 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : D.H. Hyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461217903
Total Pages : 323 pages
Book Rating : 4.4/5 (612 download)
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.
Author : Marek Kuczma
Publisher : Cambridge University Press
ISBN 13 : 9780521355612
Total Pages : 580 pages
Book Rating : 4.3/5 (556 download)
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.
Author : Antal Járai
Publisher : Springer Science & Business Media
ISBN 13 : 038724414X
Total Pages : 367 pages
Book Rating : 4.3/5 (872 download)
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.
Author : N. H. Bingham
Publisher : Cambridge University Press
ISBN 13 : 9780521379434
Total Pages : 518 pages
Book Rating : 4.3/5 (794 download)
Download or read book Regular Variation written by N. H. Bingham and published by Cambridge University Press. This book was released on 1989-06-15 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of the theory and applications of regular variation.
Author : Christopher G. Small
Publisher : Springer Science & Business Media
ISBN 13 : 0387489010
Total Pages : 139 pages
Book Rating : 4.3/5 (874 download)
Download or read book Functional Equations and How to Solve Them written by Christopher G. Small and published by Springer Science & Business Media. This book was released on 2007-04-03 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.
Author : Valeriĭ V. Buldygin
Publisher : Springer
ISBN 13 : 3319995375
Total Pages : 482 pages
Book Rating : 4.3/5 (199 download)
Download or read book Pseudo-Regularly Varying Functions and Generalized Renewal Processes written by Valeriĭ V. Buldygin and published by Springer. This book was released on 2018-10-12 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.
Author : Sui Sun Cheng
Publisher : World Scientific
ISBN 13 : 9814471720
Total Pages : 296 pages
Book Rating : 4.8/5 (144 download)
Download or read book Analytic Solutions Of Functional Equations written by Sui Sun Cheng and published by World Scientific. This book was released on 2008-03-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.
Author : Stefan Czerwik
Publisher : World Scientific
ISBN 13 : 9814489506
Total Pages : 421 pages
Book Rating : 4.8/5 (144 download)
Download or read book Functional Equations And Inequalities In Several Variables written by Stefan Czerwik and published by World Scientific. This book was released on 2002-05-14 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with — for the first time in the mathematical literature. The book contains many fresh results concerning those problems.
Author : Enrique Castillo
Publisher : CRC Press
ISBN 13 : 9780824787172
Total Pages : 354 pages
Book Rating : 4.7/5 (871 download)
Download or read book Functional Equations and Modelling in Science and Engineering written by Enrique Castillo and published by CRC Press. This book was released on 1992-05-27 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides engineers and applied scientists with some selected results of functional equations and their applications, with the intention of changing the way they think about mathematical modelling. Many of the proofs are simplified or omitted, so as not to bore or confuse engineers. Functional equati
Author : J. Aczél
Publisher : Springer Science & Business Media
ISBN 13 : 9400937490
Total Pages : 175 pages
Book Rating : 4.4/5 (9 download)
Download or read book A Short Course on Functional Equations written by J. Aczél and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently I taught short courses on functional equations at several universities (Barcelona, Bern, Graz, Hamburg, Milan, Waterloo). My aim was to introduce the most important equations and methods of solution through actual (not artifi cial) applications which were recent and with which I had something to do. Most of them happened to be related to the social or behavioral sciences. All were originally answers to questions posed by specialists in the respective applied fields. Here I give a somewhat extended version of these lectures, with more recent results and applications included. As previous knowledge just the basic facts of calculus and algebra are supposed. Parts where somewhat more (measure theory) is needed and sketches of lengthier calcula tions are set in fine print. I am grateful to Drs. J. Baker (Waterloo, Ont.), W. Forg-Rob (Innsbruck, Austria) and C. Wagner (Knoxville, Tenn.) for critical remarks and to Mrs. Brenda Law for care ful computer-typing of the manuscript (in several versions). A note on numbering of statements and references: The numbering of Lemmata, Propositions, Theorems, Corollaries and (separately) formulae starts anew in each section. If quoted in another section, the section number is added, e.g. (2.10) or Theorem 1.2. References are quoted by the last names of the authors and the last two digits of the year, e.g. Daroczy-Losonczi [671. 1 1. An aggregation theorem for allocation problems. Cauchy equation for single-and multiplace functions. Two extension theorems.
Author : J. Aczél
Publisher : Academic Press
ISBN 13 : 0080955258
Total Pages : 534 pages
Book Rating : 4.0/5 (89 download)
Download or read book Lectures on Functional Equations and Their Applications written by J. Aczél and published by Academic Press. This book was released on 1966-01-01 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
Author : Themistocles M. Rassias
Publisher : Springer Science & Business Media
ISBN 13 : 1461400554
Total Pages : 744 pages
Book Rating : 4.4/5 (614 download)
Download or read book Functional Equations in Mathematical Analysis written by Themistocles M. Rassias and published by Springer Science & Business Media. This book was released on 2011-09-18 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.
Author : Alexander S. Mechenov
Publisher : Springer
ISBN 13 : 9780387505190
Total Pages : 0 pages
Book Rating : 4.5/5 (51 download)
Download or read book Pseudosolution of Linear Functional Equations written by Alexander S. Mechenov and published by Springer. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the book there are introduced models and methods of construction of pseudo-solutions for the well-posed and ill-posed linear functional equations circumscribing models passive, active and complicated experiments. Two types of the functional equations are considered: systems of the linear algebraic equations and linear integral equations. Methods of construction of pseudos6lutions are developed in the presence of passive right-hand side errors for two types of operator errors: passive measurements and active representation errors of the operator, and all their combinations. For the determined and stochastic models of passive experiments the method of the least distances of construction of pseudosolutions is created, the maximum likelihood method of construction of pseudosolutions is applied for active experiments, and then methods for combinations of models of regression, of passive and of active experiments are created. We have constructed regularized variants of these methods for systems of the linear algebraic equations with the degenerated matrices and for linear integral equations of the first kind. In pure mathematics, the solution techniques of the functional equations with exact input data more often are studied. In applied mathematics, problem consists in construction of pseudosolutions, that is, solution of the hctional equations with perturbed input data. Such problem in many cases is incomparably more complicated. The book is devoted to a problem of construction of a pseudosolution (the problem of a parameter estimation) in the following fundamental sections of applied mathematics: confluent models passive, active and the every possible mixed experiments.
Author : J. Aczel
Publisher : Springer
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.3/5 (91 download)
Download or read book On Applications and Theory of Functional Equations written by J. Aczel and published by Springer. This book was released on 1969 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1040092934
Total Pages : 660 pages
Book Rating : 4.0/5 (4 download)
Download or read book Handbook of Exact Solutions to Mathematical Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2024-08-26 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
