Some convergence results for modified SP-iteration scheme in hyperbolic spaces

Abstract

In this paper, we prove some strong and -convergence theorems for a modified SP-iteration scheme for total asymptotically nonexpansive mappings in hyperbolic spaces by employing recent technical results of Khan et al. (Fixed Point Theory Appl. 2012:54, 2012. The results presented here extend and improve some well-known results in the current literature. 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.…”

“…(i) If {T i } i∈ and {S i } i∈ are asymptotically nonexpansive self-mappings on K, and the iterative process ( [20], respectively, when r = 3 and α in = 0 and S 1 = S 2 = · · · = S r = T are self-mappings. (iv) If the uniformly convex hyperbolic spaces reduce to CAT(0) spaces, r = 3, α in = 0, and S n 1 = S n 2 = · · · = S n r = T , where T is a nonexpansive mappings on K ⊂ X, then Theorem 2.4, Lemma 3.2, and Theorem 3.3 reduce to Theorems 1-3 in [19], respectively.…”

“…When r = 3 and α in = 0, (1.2) is equivalent to the iterative process introduced and studied by Noor [16], which was dealt with variational inequalities in Hilbert spaces. Moreover, Sahin and Basarir [20] considered a unified treatment regarding iterative process for total asymptotically nonexpansive mapping in hyperbolic spaces. For more detail, refer to [19,24] and the references therein.…”

A one-step implicit iterative process for a finite family of I-nonexpansive mappings in Kohlenbach hyperbolic spaces

“…Later on, some authors discussed the convergence of the iterative process in hyperbolic spaces (see, for example, [14][15][16][17]). Motivated by the above facts, in this paper we define a new algorithm as follows:…”

Strong and Δ-Convergence of a Faster Iteration Process in Hyperbolic Space

“…In [9], Khan et al continued the investigation of ∆-convergence in the general setup of hyperbolic spaces. Later on, some authors discussed the convergence of the iterative process in hyperbolic spaces (see, for example, [5,20]). Now, we collect some basic concepts.…”