This volume contains the Proceedings of the Special Session on FIXED
POINT THEORY AND APPLICATIONS held during the 86th Summer Meeting of the
American Mathematical Society, which took place at the University of Toronto
during August 21-26, 1982.
The theory of contractors and contractor directions is developed and used
to obtain existence theory under rather weak conditions.
Theorems on the existence of fixed points of nonexpansive mappings and
the convergence of the sequence of iterates of nonexpansive and quasi-
nonexpansive mappings are given.
Degree of mapping and its generalizations are given in detail. A class
of eventually condensing mappings is studied and multivalued condensing
mappings with multiple fixed potnts are also given.
Topological fixed points including the study of the Nielsen number of a
selfmap on a compact surface, extensions of a well-known result of
Krasnosebskii's Compression of a Cone Theorem, are given. Also, fixed points,
antipodal points, coincidences of multifunctions are discussed.
Several results with applications in the field of partial differential
equations are given.
Application of fixed point theory in the area of Approximation Theory is
As organizers of the Special Session we wish to thank Memorial University
of Newfoundland for support and, in particular, the Department of Mathematics
and Statistics, the Vice-President (Academic), Dr. E.R.W. Neale, and the Dean
of the School of Graduate Studies, Dr. F.A. Aldrich. We also want to thank
all those who helped before and after the conference. Our special thanks go
to all participants whose contributions made this Special Session a success.
As editors of the Proceedings, we wish to express our appreciation to all
contributors for their help and kind cooperation. We also thank Miss Yvonne
MacNeil for the typing of the manuscripts for offset printing. Finally, we
thank Dr. R. James Milgram for including our Proceedings in the Contemporary
Mathematics series of the American Mathematical Society and to the Editorial
Staff of the Society for their cooperation.
St. John's, Newfoundland
April , 1983