Sum of non-linear operators with fixed points.

Abstract

Chapter I gives the necessary preliminaries which may be found in most functional analysis texts. The theorems of Sadovskii [31] and Schauder [32] are also given in this chapter. -- In Chapter II a systematic and up to date summary of known results and the most recent papers dealing with a sum of non-linear operators with fixed points (i.e. Ax + Bx = x) is given. An attempt is made where possible to classify these results by spaces (i.e. Banach, Uniformly Convex Banach, Reflexive Banach, and Hilbert). Some results hold in more than one space and hence this classification is not strictly adhered to. -- In Section 2.5 some general results due to Petryshyn [28] are given and in Section 2.6 semicontractions with fixed points are discussed.