Convergence Analysis of Picard Thakur Hybrid Iterative Scheme for α-Nonexpansive Mappings in Uniformly Convex Banach Spaces

Abstract In this paper, we investigate the convergence behavior of fixed points for generalized α-nonexpansive mappings through Picard-Thakur hybrid iterative scheme. We establish both weak and strong convergence results for generalized α-nonexpansive mappings in uniformly convex Banach space. Through a numerical example, we demonstrate that the Picard-Thakur hybrid iterative scheme converges faster than other well-known schemes. Moreover, we present a data dependence result and provide a numerical example for the data dependence. The results obtained are extend and generalized the corresponding results in the existing literature. 2010 Mathematics Subject Classification. 47H09, 47H10, 24H25.