Abstract. The purpose of this paper is to study convergence of a newly defined modified S-iteration process to a common fixed point of two asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space. We give a sufficient condition for convergence to a common fixed point and establish some strong convergence theorems for the said iteration process and mappings under suitable conditions. Our results extend and improve many known results from the existing literature.

In this paper, we study strong convergence of multi-step iterations with errors for a finite family of generalized asymptotically quasinonexpansive mappings in the framework of convex metric spaces. The new iteration scheme includes modified Mann and Ishikawa iterations with errors, the three-step iteration scheme of Xu and Noor as special cases in Banach spaces. Our results extend and generalize many known results from the current literature.

Abstract. In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.

In this paper, we establish some strong convergence theorems of modified general composite implicit random iteration process to a common random fixed point for a finite family of asymptotically quasi-nonexpansive in the intermediate sense random operators.Keywords. Asymptotically quasi-nonexpansive in the intermediate sense random operator, modified general composite implicit random iteration process, common random fixed point, strong convergence, separable uniformly convex Banach space.

The purpose of this paper is to study modified S-iteration process and investigate the existence and convergence theorems in the setting of CAT(0) spaces for a class of mappings which is wider than that of asymptotically nonexpansive mappings. Our results generalize, unify and extend several comparable results in the existing literature. MSC: 54H25; 54E40