In this paper we give the strong and ∆-convergence theorems of the modified S-iteration and the modified two-step iteration processes for total asymptotically nonexpansive mappings on a CAT(0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature.

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

In this paper, we give strong convergence theorems for the modified S-iteration process of asymptotically quasi-nonexpansive mappings on a CAT(0) space which extend and improve many results in the literature. MSC: Primary 47H09; secondary 47H10

In this paper, we study the strong and -convergence theorems of SP-iteration for nonexpansive mappings on a CAT(0) space. Our results extend and improve many results in the literature. MSC: 47H09; 47H10

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