New Integrals Proceedings of the Henstock Conference held in Colerai
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1419 RS. Bullen R'f. Lee J.L. Mawhin R Muldowney WF: Pfeffer (Eds.)
New Integrals Proceedings of the Henstock Conference held in Coleraine, Northern Ireland, August 9-12, 1988
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Editors
Peter S. Bullen Department of Mathematics, University of British Columbia Vancouver, British Columbia Canada V6T 1Y4 PengYee Lee Department of Mathematics, National University of Singapore Singapore 0511, Republic of Singapore Jean L. Mawhin Departement de Mathematiques, Universite Catholique de Louvain 2 chemin du Cyclotron, 1348 Louvain-La-Neuve, Belgium Patrick Muldowney Magee College, University of Ulster Londonderry BT48 7JL, Northern Ireland Washek F. Pfeffer Department of Mathematics, University of California Davis, CA 95616, USA
Mathematics Subject Classification (1980): MR26A39 ISBN 3-540-52322-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-52322-7 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1990 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper
PREFACE
The Twelfth Summer Symposium in Real Analysis, August 9-12 1988, was held at the Coleraine campus of the University of Ulster. The theme of the conference was new integrals and related subjects, with particular reference to the generalised Riemann integral of R. Henstock and J. Kurzweil. This volume contains a brief introduction to the theme by R. Henstock, and a survey article by S. Foglio.
In holding the conference, the support of the following is acknowledged: The Royal Society, London Mathematical Society, Royal Irish Academy, Institute of Mathematics and its Applications, Department of Education (UK), Editorial Board of Real Analysis Exchange, University of Ulster, Ulster Bank, the Bushmill's Distillery and the Northern Ireland Tourist Board.
The editors express their gratitude to Mr. Gerry Shannon, Mathematics Department, University of Ulster, for his contribution to the production of these proceedings.
In addition, thanks are due to Frank Cassidy, Mike Davison, Joan Shannon, Maire Mclxeever, Leanne Woods and Chris Butler for their help.
P.M.
CONTENTS
P. Muldowney: About Ralph Henstock R.. Henstock: Introduction to the new integrals P. S. Bullen: Some applications of a theorem of Marcinkiewicz Chew T. S.: The superposition of operators in the space of Henstock-Kurzweil integrable functions S. F. L. de Fogli
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