Functional Equations and Inequalities with Applications

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering.
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.
The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition.

List of contents

Basic Equations: Cauchy and Pexider Equations.- Matrix Equations.- Trigonometric Functional Equations.- Quadratic Functional Equations.- Characterization of Inner Product Spaces.- Stability.- Characterization of Polynomials.- Nondifferentiable Functions.- Characterization of Groups, Loops, and Closure Conditions.- Functional Equations from Information Theory.- Abel Equations and Generalizations.- Regularity Conditions-Christensen Measurability.- Difference Equations.- Characterization of Special Functions.- Miscellaneous Equations.- General Inequalities.- Applications.

Summary

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering.

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.

The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition.

Additional text

From the reviews:
“This book should be of considerable interest for students and scholars working on functional equations. … the chapters treat in detail classical subjects such as Cauchy trigonometric and quadratic functional equations and present most recent results from the literature. … a comprehensive bibliography of more than 800 titles conclude this interesting book.” (Gian Luigi Forti, Mathematical Reviews, Issue 2010 e)
“In seventeen chapters and on the order of 800 pages (yikes!) we are presented with what must surely be something of an encyclopaedic treatment of the according topics. … To be sure, Kannappan’s book presents us with a most useful vade mecum for many mathematicians (not just arithmeticians) as well as various users of mathematics … .” (Michael Berg, The Mathematical Association of America, December, 2009)
“This is a comprehensive, almost encyclopedic treatment of most of the classical topics of functional equations. … the author gives references to books and survey articles. So if you want information about a topic in the field of functional equations and its history, this monograph is an obvious and good place to consult for classical results, applications and references.” (Henrik Stetkaer, Zentralblatt MATH, Vol. 1178, 2010)
“This is an encyclopaedic treatment of functional equations and inequalities by one of the leading experts in the field. … The book will be of interest not only to mathematicians but also to scientists and engineers interested in certain aspects of the field. It also contains a very substantial list of references with more than 800 entries.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)
“A laudable aim of the book is to provide scientists with some selected results of functional equations which can be useful in their subject areas. … The well-written text is a careful … exposition of functional equations, and istherefore very useful for anyone who wishes to study this very interesting and growing area of mathematics. With 841 research items being listed in the bibliography, and separate indices for authors and subjects, the book is also a useful source for reference even for the specialists.” (Peter Shiu, The Mathematical Gazette, Vol. 95 (532), March, 2011)

Report

From the reviews:
"This book should be of considerable interest for students and scholars working on functional equations. ... the chapters treat in detail classical subjects such as Cauchy trigonometric and quadratic functional equations and present most recent results from the literature. ... a comprehensive bibliography of more than 800 titles conclude this interesting book." (Gian Luigi Forti, Mathematical Reviews, Issue 2010 e)
"In seventeen chapters and on the order of 800 pages (yikes!) we are presented with what must surely be something of an encyclopaedic treatment of the according topics. ... To be sure, Kannappan's book presents us with a most useful vade mecum for many mathematicians (not just arithmeticians) as well as various users of mathematics ... ." (Michael Berg, The Mathematical Association of America, December, 2009)
"This is a comprehensive, almost encyclopedic treatment of most of the classical topics of functional equations. ... the author gives references to books and survey articles. So if you want information about a topic in the field of functional equations and its history, this monograph is an obvious and good place to consult for classical results, applications and references." (Henrik Stetkaer, Zentralblatt MATH, Vol. 1178, 2010)
"This is an encyclopaedic treatment of functional equations and inequalities by one of the leading experts in the field. ... The book will be of interest not only to mathematicians but also to scientists and engineers interested in certain aspects of the field. It also contains a very substantial list of references with more than 800 entries." (M. Kunzinger, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)
"A laudable aim of the book is to provide scientists with some selected results of functional equations which can be useful in their subject areas. ... The well-written text is a careful ... exposition of functional equations, and istherefore very useful for anyone who wishes to study this very interesting and growing area of mathematics. With 841 research items being listed in the bibliography, and separate indices for authors and subjects, the book is also a useful source for reference even for the specialists." (Peter Shiu, The Mathematical Gazette, Vol. 95 (532), March, 2011)

Product details

• Authors: Palaniappan Kannappan, Pl Kannappan, Pl. Kannappan
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2016
• EAN: 9781489979025
• ISBN: 978-1-4899-7902-5
• No. of pages: 810
• Dimensions: 155 mm x 44 mm x 235 mm
• Weight: 1258 g
• Illustrations: XXIII, 810 p.
• Series: Springer Monographs in Mathematics; Springer Monographs in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Mathematics and Statistics, Applications of Mathematics, Functional Analysis, Difference equations, Functional equations, Difference and Functional Equations, Engineering mathematics, Applied mathematics, Functional analysis & transforms