A generalization of a fixed point theorem in probabilistic locally convex spaces
The existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.
We establish a fixed point theorem for a continuous function , where is a Banach space and . Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.