Abstract
In this paper, we prove some strong and Δ-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.
Highlights
1 Introduction and preliminaries Iterative schemes play a key role in approximating fixed points of nonlinear mappings
The concept of p-uniformly convexity has been defined by Naor et al [ ] and its nonlinear version for p = in hyperbolic spaces was studied by Khan [ ]
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Summary
Introduction and preliminariesIterative schemes play a key role in approximating fixed points of nonlinear mappings. It has been shown that every total asymptotically nonexpansive mapping defined on a nonempty bounded closed convex subset of a complete uniformly convex hyperbolic space always has a fixed point W (zn, T = W (yn, nzn, βn), T nyn, αn where K is a nonempty, closed and convex subset of a complete uniformly convex hyperbolic space X with monotone modulus of uniform convexity and T : K → K is a uniformly L-Lipschitzian and total asymptotically nonexpansive mapping.
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