Convergence theorems for total asymptotically nonexpansive non-self mappings in "Equation missing" spaces

Abstract

In this paper, we introduce the concept of total asymptotically nonexpansive nonself mappings and prove the demiclosed principle for this kind of mappings in CAT(0) spaces. As a consequence, we obtain a -convergence theorem of total asymptotically nonexpansive nonself mappings in CAT(0) spaces. Our results extend and improve the corresponding recent results announced by many authors. MSC: 47H09; 47J25

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.…”

“…However, in general, the converse is not true. Indeed, Wang et al [30] introduced the class of total asymptotically nonexpansive nonself-mappings, and generalized and extended several classes of asymptotically nonexpansive mappings. For more detail, see, for example, [29,32] and the references therein.…”

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]). …”

Strong convergence of a modified SP-iteration process for generalized asymptotically quasi- nonexpansive mappings in CAT(0) spaces

“…In 2008, Kirk and Panyanak [12] specialized Lim's concept to CAT(0) spaces and proved that it is very similar to weak convergence in the Banach space setting. Every nonexpansive (single-valued) mapping defined on closed bounded convex subset of complete CAT(0) space always has a fixed point, since then the fixed point theory in CAT(0) space has been rapidly developed and many paper has appeared [3,5,6,8,10,13,17,18,19,20].…”