ITERATIVE CONSTRUCTION OF FIXED POINTS OF ASYMPTOTIC 1-SET CONTRACTIONS IN BANACH SPACES

Abstract

We prove theorems on the existence of fixed points and the structure of fixed point sets for asymptotic 1-set contraction mappings T on certain subsets of Banach spaces by assuming some condition on T. We also prove some fixed point theorems for a sum of asymptotic 1-set contraction and compact (strongly continuous) mappings in real Banach spaces (reflexive real Banach spaces).