General Inequalities 7: 7th International Conference at Oberwolfach, November 13–18, 1995

397 Pages·1997·33.598 MB·English

by  Pavel Drábek, Hans P. Heinig, Alois Kufner (auth.), Catherine Bandle, William N. Everitt, Laszlo Losonczi, Wolfgang Walter (eds.)

ISNM
International Series of
Numerical Mathematics
Vol. 123
Managing Editors:
K.-H. Hoffmann, München
D. Mittelmann, Tempe
Associate Editors:
R.E. Bank, La Jolla
H. Kawarada, Chiba
R.J. LeVeque, Seattle
C. Verdi, Milano
Honorary Editor:
J. Todd, Pasadena
General Inequalities 7
7th International Conference at Oberwolf ach, November 13-18 ,1995
Edited by
C. Bandle
W.N. Everitt
L. Losonczi
W. Walter
Springer Basel AG
Editors:
Catherine Bandle William N. Everitt
Institute of Mathematics School of Mathematics and Statistics
University of Basel University of Birmingham
Rheinsprung 21 Edgbaston
4051 Basel Birmingham B15 2TT
Switzerland England, U.K.
e-mail: bandle @math.unibas.cn e-mail: [email protected]
Laszlo Losonczi Wolfgang Walter
Department of Mathematics and Computer Science Institute of Mathematics I
Kuwait University University of Karlsruhe
P.O. Box 5969 Kaiserstr. 12
13060 Safat 76128 Karlsruhe
Kuwait Germany
e-mail: [email protected] e-mail: waiter@ma 1 ws 1 .mathematik.uni-karlsruhe.de
1991 Mathematics Subject Classification 26A51, 26DXX, 39B72, 35P15, 52A41, 15A42
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
General inequalities 7 / 7th International Conference on
General Inequalities, Oberwolfach, November 13-18, 1995. Ed.
by C. Bandle ... - Basel; Boston ; Berlin : Birkhäuser, 1997
(International series of numerical mathematics ; Vol. 123)
ISBN 978-3-0348-9837-9 ISBN 978-3-0348-8942-1 (eBook)
DOI 10.1007/978-3-0348-8942-1
NE: Bandle, Catherine [Hrsg.]; Internationale Tagung über Allgemeine
Ungleichungen <7, 1995, Oberwolfach>; GT
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© 1997 Springer Basel AG
Originally published by Birkhäuser Verlag in 1997
Softcover reprint of the hardcover 1st edition 1997
Printed on acid-free paper produced from chlorine-free pulp. TCF °°
Cover design: Heinz Hiltbrunner, Basel
ISBN 978-3-0348-9837-9
987654321
Preface
Inequalities continue to play an essential role in mathematics. The subject is per
haps the last field that is comprehended and used by mathematicians working in
all the areas of the discipline of mathematics. Since the seminal work Inequalities
(1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend
and sharpen the earlier classical inequalities. New inequalities are discovered ev
ery year, some for their intrinsic interest whilst others flow from results obtained
in various branches of mathematics. So extensive are these developments that a
new mathematical periodical devoted exclusively to inequalities will soon appear;
this is the Journal of Inequalities and Applications, to be edited by R.P. Agar
wal. Nowadays it is difficult to follow all these developments and because of lack
of communication between different groups of specialists many results are often
rediscovered several times. Surveys of the present state of the art are therefore in
dispensable not only to mathematicians but to the scientific community at large.
The study of inequalities reflects the many and various aspects of mathemat
ics. There is on the one hand the systematic search for the basic principles and
the study of inequalities for their own sake. On the other hand the subject is a
source of ingenious ideas and methods that give rise to seemingly elementary but
nevertheless serious and challenging problems. There are many applications in a
wide variety of fields from mathematical physics to biology and economics.
The main goal of the General Inequalities meetings held at Oberwolfach is to
bring together research workers from many parts of the globe, working in different
and seemingly unconnected areas but interested in the many different aspects of
inequalities. These meetings have now a long tradition extending over more than
twenty years; the first meeting took place in 1976 inspired by the efforts of J. Aczel,
G. Aumann, E.F. Beckenbach, R. Bellman and W. Walter.
This volume contains the proceedings of the General Inequalities 7 meeting
held at Oberwolfach in 1995. It is conceived in the spirit of the preceding volumes in
the sense that it not only contains the latest results presented by the participants,
but is also a useful reference book for both lecturers and research workers. The
material is ordered in seven chapters from Inequalities in Analysis to Applications,
and ends in the same way as the preceding volumes with a lively chapter entitled
Problems and Remarks. The contributions here given reflect the ramifications of
general inequalities into many areas of mathematics, and also present a synthesis
of results in both theory and practice.
During the GI 7 meeting a reception was held in honour of Professor Wolf
gang Walter to mark his retirement from the GI Committee, and to recognise his
VI Preface
unique and dedicated service to the sequence of meetings at Oberwolfach. Partic
ular mention was made of his tireless efforts in serving as Editor of the series of
Proceedings for these meetings; these volumes, prepared with metriculous atten
tion to detail, now form an invaluable collection of results in the general field of
inequalities in mathematics.
The dedicated labours of Mrs. Irene Jendrasik have been essential to the
production of this volume in its final form; with her expertise and professional
skill she processed all the 'lEX files and so presented them in a uniform manner.
The Editors thank her warmly for this excellent contribution.
The Editors are also indebted to Dr. Gerd Herzog, Dr. Wolfgang Reichel,
and Dr. Ch. Schmoeger who assisted in the technical details and undertook all the
necessary proof reading.
The inspiring atmosphere and excellent facilities of the Mathematical
Research Institute at Oberwolfach contributed essentially to the success of the
meeting.
November 1996 C. Bandle
W.N. Everitt
1. Losonczi
W. Walter
Participants
J. ACZEL, University of Waterloo, Waterloo, Ontario, Canada
R.P. AGARWAL, National University of Singapore, Kent Ridge, Singapore
C.D. AHLBRANDT, University of Missouri, Columbia, Missouri, USA
H. ALZER, Waldbral, Germany
M. S. ASHBAUGH, University of Missouri, Columbia, Missouri, USA
R. BADORA, Silesian University, Katowice, Poland
C. BANDLE, Universitat Basel, Basel, Switzerland
R. BENGURIA, Pontificia University Catolica, Santiago, Chile
C. BENNEWITZ, University of Lund, Lund, Sweden
M. BOHNER, University of Ulm, Ulm, Germany
A. BRILLARD, University of Haute Alsace, Mulhouse, France
F. BROCK, Universitat zu Kaln, Kaln, Germany
B.M. BROWN, University of Wales, Cardiff, Wales, U.K.
R.C. BROWN, University of Alabama, Tuscaloosa, Alabama, USA
A. CLAUSING, Westfal. Wilhelms-Universitat, Munster, Germany
W. EICHHORN, Universitat Karlsruhe, Kalsruhe, Germany
M. ESSEN, University of Uppsala, Uppsala, Sweden
W.N. EVERITT, University of Birmingham, Birmingham, England
J. FLECKINGER, University of Toulouse I, Toulouse, France
M. FLUCHER, Universitat Basel, Basel, Switzerland
T. FURUTA, Science University of Tokyo, Tokyo, Japan
R. GER, Silesian University, Katowice, Poland
M. GOLDBERG, Israel Institute of Technology, Haifa, Israel
W . HAYMAN, Imperial College of Science and Technology,
London, England
D.B. HINTON, University of Tennessee at Knoxville, Knoxville,
Tennessee, USA
K. KARTAK, Technical University of Prague, Prague, Czech
Republic
Vlll Participants
B. KAWOHL, Universitiit zu Kaln, Kaln, Germany
H. KONIG, Universitiit des Saarlandes, Saarbrucken, Germany
H. KONIG, Universitiit Kiel, Kiel, Germany
A. KUFNER, Ceskoslovenska Akademie Ved, Praha, Czech
Republic
L. LOSONCZI, Kuweit University, Kuwait
E.R. LOVE, University of Melbourne, Parkville, Victoria,
Australia
M. MARCUS, Israel Institute of Technology, Haifa, Israel
J. MATKOWSKI, Technical University, Bielsko-Biala, Poland
G.V. MILOVANOVIC, University of Nis, Nis, Yugoslavia
R.N. MOHAPATRA, University of Central Florida, Orlando, Florida, USA
G. NASRI-RoUDSARI, Rhein.-Westf. Techn. Hochschule, Aachen, Germany
R.J. NESSEL, Rhein.-Westf. Techn. Hochschule, Aachen, Germany
ZS. PALES, Lajos Kossuth University, Debrecen, Hungary
C.E.M. PEARCE, University of Adelaide, Adelaide, Australia
J.E. PECARIC, Faculty of Technology, Zagreb, Yugoslavia
M. PLUM, Universitiit Karlsruhe, Karlsruhe, Germany
TH.M. RASSIAS, National Technical University of Athens, Athens, Greece
J. RATZ, Universitiit Bern, Bern, Switzerland
W. REICHEL, Universitiit Karlsruhe, Karlsruhe, Germany
D.C. RUSSELL, Ventnor, England
S. SAITOH, Gunma University, Kiryu, Japan
G. TALENTI, Universita degli Studi, Firenze, Italy
P. VOLKMANN, U niversitiit Karlsruhe, Karlsruhe, Germany
W. WALTER, Universitiit Karlsruhe, Karlsruhe, Germany
A. ZETTL, Northern Illinois University, DeKalb, Illinois, USA
Contents
Preface.................................................................. v
Participants .............................................................. VB
INEQUALITIES IN ANALYSIS
P. DRABEK, H. HEINIG AND A. KUFNER
Higher dimensional Hardy inequality 3
GRADIMIR V. MILOVANOVIC
Integral inequalities for algebraic polynomials 17
C.E.M. PEARCE, J. PECARIC AND S. VAROSANEC
Inequalities of GauB-Minkowski type ................................ 27
SABUROU SAITOH
Natural norm inequalities in nonlinear transforms. . . . . . . . . . . . . . . . . . . . 39
INEQUALITIES FOR MATRICES AND DISCRETE PROBLEMS
MARTIN BOHNER
Positive definiteness of discrete quadratic functionals 55
MOSHE GOLDBERG
Stable norms - Examples and remarks 61
TAKAYUKI FURUTA
Applications of order preserving inequalities to a generalized
relative operator entropy ............................................ 65
J. PECARIC AND B. MOND
The arithmetic mean - the geometric mean and related
matrix inequalities .................................................. 77
x Contents
INEQUALITIES FOR EIGENVALUE PROBLEMS
M.S. ASHBAUGH, R.D. BENGURIA AND R.S. LAUGESEN
Inequalities for the first eigenvalues of the clamped plate
and buckling problems .............................................. 95
MARK S. ASHBAUGH AND RAFAEL D. BENGURIA
One the Payne-P6lya-Weinberger conjecture on the
n-dimensional sphere ................................................ 111
R.C. BROWN AND D.B. HINTON
Norm eigenvalue bounds for some Sturm-Liouville problems.......... 129
W.N. EVERITT, M. MOLLER AND A. ZETTL
Discontinuous dependence of the n-th Sturm-Liouville problem 145
INEQUALITIES FOR DIFFERENTIAL OPERATORS
HORST ALZER
Note on Wirtinger's inequality 153
RAVI P. AGARWAL AND PETER Y.H. PANG
Opial-type inequalities involving higher order partial derivatives
of two functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157
B.M. BROWN AND N.G.J. DIAS
The HELP type integral inequalities for 2nth order
differential operators ................................................ 179
MOSHE MARCUS
An estimate related to the Gagliardo-Nirenberg inequality 193
FRANCESCO MUGELLI AND GIORGIO TALENTI
Sobolev inequalities in 2-dimensional hyperbolic space 201
CONVEXITY
ROMAN BADORA
On the separation with n-additive functions 219
JANUSZ MATKOWSKI AND JURG RATZ
Convexity of power functions with respect to symmetric
homogeneous means................................................. 231