△-convergence for mixed-type total asymptotically nonexpansive mappings in hyperbolic spaces

Abstract

In this paper, we prove some -convergence theorems in a hyperbolic space. A mixed Agarwal-O'Regan-Sahu type iterative scheme for approximating a common fixed point of total asymptotically nonexpansive mappings is constructed. Our results extend some results in the literature. MSC: 47H09; 49M05

On strong and Δ -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces

“…Recently, Panyanak [25] studied the existence theorems, the demiclosed principle, ∆-convergence and strongly convergence theorems for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces. Moreover, there were many authors who have studied about this mappings, (see e.g., [4,7,8,17,25,31,33,34,35,36,37]). …”

\Delta-convergence for common fixed points of two asymptotically nonexpansive nonself mappings in hyperbolic spaces

“…In recent years, Yang and Zhao [2] studied the strong andconvergence theorems for total asymptotically nonexpansive nonself-mappings in CAT(0) spaces. Wan [3] proved some -convergence theorems in a hyperbolic space, in which a mixed Agarwal-O'Regan-Sahu type iterative scheme for approximating a common fixed point of totally asymptotically nonexpansive mappings was constructed. Li and Liu [4] modified a classical Kuhfittig iteration algorithm in the general setup of hyperbolic space, and prove aconvergence theorem for an implicit iterative scheme.…”

Approximating Fixed Point of Two Generalized Asymptotically Non Expansive Mapping Through Kuhfitting Iterative Process in Hyperbolic Spaces.

“…In recent years, Yang and Zhao [25] studied the strong and ∆convergence theorems for total asymptotically nonexpansive nonself-mappingsin CAT(0) spaces. Wan [23] proved some ∆ convergence theorems in a hyperbolic space, in which a mixed Agarwal-O'Regan-Sahu type iterative scheme for approximating a common fixed point of totally asymptotically nonexpansive mappings was constructed. Li and Liu [12] modified a classical Kuhfittig iteration algorithm in the general set up of hyperbolic space, and prove a ∆ convergence theorem for an implicit iterative scheme.…”