FIXED POINT THEOREMS OF STRICT SET-CONTRACTIONS VIA ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

Abstract

By using ordinary differential equations in Banach spaces, a topological degree for strict set contractions is defined and furthermore some new fixed point theorems are obtained. The degree is then proved to be the well-known Leray-Schauder degree for completely continuous operators and finally it is used to compute the Leray-Schauder degree for completely continuous operators with gradient forms.