A CONTRACTION PRINCIPLE IN WEAKLY CAUCHY NORMED SPACES

Abstract

In this paper we establish a general contraction principle in any normed space X which is weakly Cauchy (see [1], [5] and [6]) but not necessarily complete and (possibly) not reflexive. Without using continuity (see Thorem 2.3 below), we prove the existence of a unique common fixed point for two weakly compatible self-mappings of a closed convex subset satisfying a contraction condition. In particular, our result generalizes and improves the main result of [5].