Dynamics of Cyclic Contractions

Abstract

Cyclic contractions generalize the usual contractivities in metric spaces and $b$-MSs. In this paper, we enhance several fixed point theorems related to cyclic (i) Banach self-maps, (ii) Chatterjea contractivities, (iii) Kannan self-mappings, (iv) Ćirić and Hardy-Rogers, and (v) Reich contractions including local versions in $b$-metric spaces while also delineating the associated dynamics. Especially noteworthy is the expansion of the results concerning both fixed and periodic points, which are substantiated across a wider spectrum of ratio values for the aforementioned cyclic contractions within this class of spaces. Additionally, the convergence of Picard iterations towards the fixed point is rigorously established.

Error was found in the paper