Approximation of point of coincidence and common fixed points of quasi-contraction mappings using the Jungck iteration scheme

Abstract

Let (X, d) be a cone metric space over a solid vector space (Y, ⪯). In this paper, we prove a convergence theorem with error estimates and localization formula for Jungck iteration process for approximating points of coincidence and common fixed points of two selfmappings T and f of X satisfying a quasi-contraction condition of the typed(Tx,Ty)⪯λco{d(fx,fy),d(fx,Tx),d(fy,Ty),d(fx,Ty),d(fy,Tx)}for all x, y ∈ X, where λ ∈ (0, 1) is a constant. Our result complements the recent result of Ding et al. [9].The main result is new even in the classical metric space setting. Moreover, this result answers an open question posed by Olaleru [17] concerning common fixed points in metric spaces.