Fixed point theorems for a sum of two mappings in locally convex spaces
Summary: Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnosel'skij 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.
uniformly asymptotically regular with respect to a map
fixed point theorem of Krasnosel'skij for a sum of contraction and compact mappings in Banach spaces
sum of asymptotically nonexpansive and continuous mappings in locally convex spaces
scientific article; zbMATH DE number 697107