Fixed Point Theorms of Operators with PPF Dependence in Banach Spaces

Abstract

**Please note that the full text is embargoed** ABSTRACT: In this paper we develop a theory of fixed points of a nonlinear operator, T, whose domain is the Banach space of continuous functions defined on an interval [a,b] with range in a Banach space E denoted by [see pdf for notation] and the range of the nonlinear operator T is in E. As we shall see delay differential equations form an important example of such a nonlinear operator. We shall obtain analogues of the contraction mapping principle, Krasnoselskii's fixed point theorem as well as a result on the convergence of iterations of quasi-nonexpansive mappings.