Modified Picard-Mann hybrid iteration process for total asymptotically nonexpansive mappings

Abstract

In this paper, using the modified hybrid Picard-Mann iteration process, we establish -convergence and strong convergence theorems for total asymptotically nonexpansive mappings on a CAT(0) space. Results established in the paper extend and improve a number of results in the literature. A numerical example is also given to examine the fastness of the proposed iteration process under different control conditions and initial points. MSC: 47H09; 47H10

Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces

“…The results presented in the paper extend and improve some recent results given in [4,5,14,19,20,24,27,29,30,33]. Some special cases are listed as follows.…”

“…Example 1.4. Let r = 2, α 1n = β 1n = 0, and α 2n = 0, then (1.2) becomes to the iteration discussed by Thakur et al [27] in CAT(0) space as follows:…”

Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space

“…They [3] further studied the iterative approximation of fixed point for total asymptotically nonexpansive mappings using a modified Krasnoselskii-Mann iteration process. Iterative approximation of fixed points of total asymptotically non-expansive mappings has also been studied by [2,13,14,19].…”

Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

“…To know the importance of different iterative algorithms for the approximation of fixed points of total asymptotically nonexpansive mappings in uniformly convex Banach spaces, CAT (0) spaces and hyperbolic spaces, we refer the interested reader to [7,11,15,21,25].…”