Rates of convergence for a class of generalized quasi contractive mappings in Kohlenbach hyperbolic spaces

Abstract

This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces, Sci. Int., 25(4) (2013), 887-891], in spaces of nonpositive sectional curvature. We aim to establish results concerning convergence characteristics of the classical iterative algorithms such as Picard, Mann, Ishikawa and Xu-Noor iterative algorithms associated with the proposed class of generalized quasi contractive operators. Moreover, we adopt the concept introduced by Berinde [Comparing Krasnosel'skii and Mann iterative methods for Lipschitzian generalized pseudo-contractions, Int. Conference on Fixed Point Theory Appl., 15-26, Yokohama Publ., Yokohama, 2004.] for a comparison of the corresponding rates of convergence of these iterative algorithms in such setting of spaces. The results presented in this paper improve and extend some recent corresponding results in the literature.