Functional Equations, Inequalities and Applications
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 equatio
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Functional Equations, Inequalities and Applications Edited by
Themistocles M. Rassias Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens, Greece
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SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-6406-6 ISBN 978-94-017-0225-6 (eBook) DOI 10.1007/978-94-017-0225-6
Printed on acid-free paper
All Rights Reserved © 2003 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2003 Softcover reprint ofthe hardcover Ist edition 2003 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilrning, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
Contents
Preface
vii
1 Hyers-Ulam stability of a quadratic functional equation in Banach modules Jae-Hyeong Bae and Won-Gil Park
1
2 Cauchy and Pexider operators in some function spaces Stefan Czerwik and K rzysztof Dlutek
11
3 The median principle for inequalities and applications Sever S. Dragomir
21
4 On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic equation II Kil- Woung Jun and Yang-Hi Lee
39
5 On the Hyers-Ulam-Rassias stability of a functional equation
67
Soon-Mo lung 6 A pair of functional inequalities of iterative type related to a Cauchy functional equation Dorota Krassowska and Janusz Matkowski 7 On approximate algebra homomorphisms
73
91
Chun-Gil Park 8 Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions Josip Pecaric and Ana Vukelic
v
105
vi
Functional Equations, Inequalities and Applications
9 On Ulam stability in the geometry of PDE's Agostino Prastaro and Themistocles M. Rassias
139
10 On certain functional equations and mean value theorems Themistocles M. Rassias and Young-Ho Kim
149
11 Some general approximation error and convergence rate estimates in statistical learning theory
159
Saburou Saitoh
12 Functional equations on hypergroups
167
Laszlo Szekelyhidi
13 The generalized Cauchy functional equation
183
Abraham A. Ungar
14 On the Aleksandrov-Rassias problem for isometric mappings
191
Shuhuang Xiang Index
223
Preface
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 geometric 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, stability of a Pexiderized quadratic equation, functi
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