Fixed points of cyclic weak contractions in metric spaces

Abstract

In this paper the well knownnotion of a cyclic contraction for a finite family of non-empty subsets of ametric space $X$ and a mapping $T$ of $X$ into $X$ (respectively, into thecollection of nonempty subsets of $X$) has been generalized. Subsequently,the above idea is used to obtain some new fixed point theorems for singleand multi-valued mappings. The results obtained herein generalize somerecent fixed point theorems.