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Introduction To Functional Equations
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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 CRC Press. This book was released on 2011-02-08 with total page 465 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 p
Book Synopsis Introduction to Functional Equations by : Costas Efthimiou
Download or read book Introduction to Functional Equations written by Costas Efthimiou and published by American Mathematical Soc.. This book was released on 2011-10-13 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Functional Equations and How to Solve Them by : Christopher G. Small
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.
Book Synopsis An Introduction to the Theory of Functional Equations and Inequalities by : Marek Kuczma
Download or read book An Introduction to the Theory of Functional Equations and Inequalities written by Marek Kuczma and published by Springer Science & Business Media. This book was released on 2009-03-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)
Book Synopsis The Cauchy-Schwarz Master Class by : J. Michael Steele
Download or read book The Cauchy-Schwarz Master Class written by J. Michael Steele and published by Cambridge University Press. This book was released on 2004-04-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.
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.
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.
Book Synopsis Applied Theory of Functional Differential Equations by : V. Kolmanovskii
Download or read book Applied Theory of Functional Differential Equations written by V. Kolmanovskii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.
Book Synopsis A Short Course on Functional Equations by : J. Aczél
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.
Book Synopsis Functional Equations by : David Leigh-Lancaster
Download or read book Functional Equations written by David Leigh-Lancaster and published by ACER Press. This book was released on 2006-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional equations provides mathematics teachers with an introduction to elementary aspects of functional equations.
Book Synopsis On the Functional Equations Satisfied by Eisenstein Series by : Robert P. Langlands
Download or read book On the Functional Equations Satisfied by Eisenstein Series written by Robert P. Langlands and published by Springer. This book was released on 2006-11-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Functions and Functional Equations by : J. Smital
Download or read book On Functions and Functional Equations written by J. Smital and published by CRC Press. This book was released on 2020-08-26 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Functions and Functional Equations introduces the main topics in iteration theory and the theory of functional equations with emphasis on applications in the fields of mathematics, physics, biology, chemistry, and electronics and mechanical engineering. The book contains many classical results as well as important, more recent results. It also includes numerous exercise and some problems that have yet to be resolved. The book is accessible to readers having a secondary level mathematical education.
Book Synopsis Topics in Functional Equations by : Titu Andreescu
Download or read book Topics in Functional Equations written by Titu Andreescu and published by . This book was released on 2020-01-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Functional Equations and Their Applications by : J. Aczel
Download or read book Lectures on Functional Equations and Their Applications written by J. Aczel and published by Courier Corporation. This book was released on 2006-02-01 with total page 548 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.
Book Synopsis Mean Value Theorems and Functional Equations by : Prasanna Sahoo
Download or read book Mean Value Theorems and Functional Equations written by Prasanna Sahoo and published by World Scientific. This book was released on 1998 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
