Functional Analysis, Approximation Theory and Numerical Analysis

340 Pages·1994·12.63 MB·English

by  John M Rassias

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Editor
John "· Rnssins
World Sclentlflc
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FUNCTIONRL
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John M. Rassias
The National Universitq of Athens
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World Scientific
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Singapore •New Jersey• London· Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P 0 Box 128, Farrer Road, Singapore 9128
USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661
UK office: 73 Lynton Mead, Totteridge, London N20 8DH
FUNCTIONAL ANALYSIS, APPROXIMATION THEORY AND
NUMERICAL ANALYSIS
Copyright © 1994 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof may not be reproduced in any form
or by any means, electronic or mechanical, including photocopying, recording or any
information storage and retrieval system now known or to be invented, without
written permissionfrom the Publisher.
For photocopying of material in this volume, please pay a copying fee through
the Copyright Clearance Center, Inc„ 27 Congress Street, Salem, MA 01970, USA.
ISBN 981-02-0737-9
Printed in Singapore by Utopia Press.
Dedicated to
Stefan Banach on his lOOth birthday,
Alexander Markowi.i: Ostrowski on his 99th birthday,
Stanislaw Marein Ulam on his 83rd birthday
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PREFACE
This volume (F.A.N.) contains various parts of Functional Analysis,
Approximation Theory and Numerical Analysis, namely: A conditional Cauchy
equation on rhombuses, spectral properties of matrices with products of
binomial coefficients as entries, optimization of functionals and application
to differential equations, an alternative Cauchy equation, generalization of
the Golab-Schinzel functional equation, and functional equations and exact
discrete solutions of ordinary differential equations. Besides it contains part
on: Shape from shading problem, approximations to analytic functions,
error estimate in non-equi-mesh spline finite strip method for thin plate
bending problem, the Hyers-Ulam stability of a functional equation containing
partial difference operators, dynamical systems and processes on Banach
infinite dimensional spaces, Banach spaces in Bergman operator theory,
characterization problems in Hilbert space, fixed point procedure in Banach
spaces, Banach algebras of pseudodifferential operators, and Banach spaces.
Finally the reader of this volume can find parts on: Ostrowski constant,
stability problem of Ulam, Gegenbauer polynomials, quasi-tridiagonal system
of linear equations, characterization of Q-algebras, and Landau 's type
inequalities.
This collection of research works is dedicated to the mathematicians: Stefan
BANACH, Alexander Markowii; OSTROWSKI, and Stanislaw Marein ULAM
for their great contributions in Mathematics, Physics, Chemistry, Biology, and
many other branches of Science.
Deep gratitude is due to all those friends and scientists who have encouraged
me to complete this book in less than four years of continuous work. My very
special thanks and appreciation to my family: Katia, Matina, and Vassiliki.
Finally 1 have to thank the consultant editor Professor J. G. Xu and the
Scientific editor Dr. Anju Goel of WORLD SCIENTIFIC for their patience
::i.nd overall cooperation to carry out this project.
John Michael Rassias, Ph.D.
Professor of Mathematics
vii
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CONTENTS
Preface vii
Stefan Banach, Alexander Markowi~ Ostrowski, Stanislaw Marein
Ulam
J. M. Rassias 1
On a Conditional Cauchy Equation on Rhombuses 5
C. Alsina and J.-L. Garcia-Roig
Spectral Properties of Matrices with Products of Binomial
Coefficients as Entries 9
L. Berg and K. Engel
Optimization of Functionals and Application to Differential
Equations 19
P C. Bhakta
On an Alternative Functional Equation in ~n 33
C. Borelli-Forti and G. L. Forti
On a Generalization of the Golab-Schinzel Functional Equation 45
N. Brillouet-Belluot
Functional Equations and Exact Discrete Solutions of Ordinary
Differential Equations 75
E. Castillo and R. Ruiz-Cobo
On Shape from Shading Problem 93
J. Chabrowski and K. Zhang
On the Approximations to Analytic Functions 107
C. C. Chang
ix