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-reac

  • PDF / 7,218,025 Bytes
  • 817 Pages / 439.37 x 666.142 pts Page_size
  • 77 Downloads / 221 Views

DOWNLOAD

REPORT


Pl. Kannappan

Functional Equations and Inequalities with Applications

Pl. Kannappan Department of Pure Mathematics University of Waterloo Waterloo ON, N2L 3G1, Canada [email protected]

ISSN 1439-7382 ISBN 978-0-387-89491-1 e-ISBN 978-0-387-89492-8 - DOI: 10.1007/978-0-387-89492-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926483 M athematics Subject Classification (2000): 39Bxx 39B72 39D05

© Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Dedication To my wife Renganayaki and grandchildren Kanna, Anand, Nila, Sarasvathi, Senthil and Sathiya

Preface

It is natural to ask what a functional equation is. But there is no easy satisfactory answer to this question. While such concepts as element, relation, mapping, operation, etc., are well defined in set theory, the principal concept set is an undefined term. It is not considered as an impediment for the growth, development, and usefulness of set theory. We are going to follow this idea and consider functional equations as an undefined concept. This is not going to be a severe roadblock to understanding, appreciating, and contributing to the growth and development of this fascinating area. As in set theory, we hope the reader will get a general insight of what this theory is about. Functional equations occur practically everywhere. Their influence and applications are felt in every field, and all fields benefit from their contact, use, and technique. The growth and development used to be influenced by their spectacular application in several areas—not only in mathematics but also in other disciplines. Applications can be found in a wide variety of fields—analysis, applied science, behavioural and social science, biology, combinatorics, computers, economics, engineering, geometry, inequalities, information theory, inner product space, physics, polynomials, psychology, reproducing scoring system, statistics, taxation, etc. Functional equations are being used with vigor in ever-increasing numbers to investigate problems in the above-mentioned areas and other fields. Even though many eminent mathematicians—including Abel (1823), Banach (1920), Cauchy (1821), Darboux (1895), Euler (1768), Ostrowski (1929), Pex