Vol. 79, No. 2, 1978

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
The common fixed point theory of singlevalued mappings and multivalued mappings

Shigeru Itoh and Wataru Takahashi

Vol. 79 (1978), No. 2, 493–508

First, in a locally convex topological vector space, a theorem is proved which extends fixed point theorems by Lau and Fan-Glicksberg. In a strictly convex Banach space, a similar result is obtained, which is a generalization of the fixed point theorem by Bohnenblust-Karlin. In a Banach space which satisfies Opial’s condition, a fixed point theorem is given that generalizes both results by Holmes-Lau-Lim and Lami Dozo. In a uniformly convex Banach space, a similar theorem is considered which extends Lim’s fixed point theorem. Finally, the existence of common fixed points of a quasi-nonexpansive mapping and a multivalued nonexpansive mapping is established by an elementary constructive method in a Hilbert space. In many cases, preliminary results on nonexpansive or quasi-nonexpansive retractions are obtained which play crucial roles in proving the above theorems.

Mathematical Subject Classification 2000
Primary: 47H10
Secondary: 47H09
Received: 3 March 1978
Revised: 15 May 1978
Published: 1 December 1978
Shigeru Itoh
Wataru Takahashi