International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 681-686

Fixed point theorems for a sum of two mappings in locally convex spaces

P. Vijayaraju

Department of Mathematics, Anna University, Madras 600 025, India

Received 2 May 1991; Revised 12 March 1992

Copyright © 1994 P. Vijayaraju. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed.