Iterative Algorithm and Δ‐Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Abstract

The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove aΔ-convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature.

A new iterative scheme in CAT(0) spaces with convergence analysis

“…Our results extend, improve, and generalize the corresponding results of [4,7,8,11,16,19,23,28,30,32,36,38] and many others.…”

“…(iv) Our results also extend and improve the corresponding results contained in [4,7,16,19,23,32,36,38] and many others from the existing literature. Now, we give some examples in support of our result.…”

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]). …”

Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems

“…Since then, some convergence theorems of many iterative algorithms for a type of such a mapping has been rapidly developed and several of articles have cited in references (see e.g. [5,9,18,28,31,32,[37][38][39]). …”