A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES

Abstract

This article presents a modified Picard-S iterative method in hyperbolic spaces. The proposed iterative method is used to approximate the common fixed point of two contractive-like mappings. We consider new concepts of data dependence and weak w2-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic spaces. We prove the strong and A-convergence results of our new algorithm for common fixed points of two mappings enriched with the condition (E). With numerical examples, we show the advantage and efficiency of the proposed method over some existing methods. Our results generalize and improve several results in the literature.