FIXED POINTS FOR MAPPINGS SATISFYING CYCLICAL CONTRACTIVE CONDITIONS

Abstract

This paper deals with mappings of the type f : Ai → Ai+1, i = 1, 2, · · ·, p + 1, with Ap+1 = Ap, where the contractive assumptions are restricted to pairs (x, y) ∈ Ai×Ai+1. Extensions of Banach’s theorem are considered as well as an extension of Caristi’s theorem. The paper concludes with a result about nonexpansive mappings in a Banach space setting.