Proximal Point Algorithms Involving Cesàro Type Mean of Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Proximal point algorithms involving fixed points of nonexpansive mappings in CAT(0)$\operatorname{CAT}(0)$ spaces

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Fixed Point Theorems for Nonself Asymptotically Nonexpansive type Mappings in CAT(0) Spaces

In this paper, we propose a three-step iteration scheme for nonself asymptotically nonexpansive type mappings in a complete CAT(0) metric space and establish necessary and sufficient conditions for convergence of this process to a fixed point of nonself asymptotically nonexpansive type mappings. We also establish a strong convergence result. These results generalize and unify many important res...

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition

Convergence Theorems for Asymptotically Nonexpansive Mappings in Banach Spaces

Let E be a uniformly convex Banach space, and let K be a nonempty convex closed subset which is also a nonexpansive retract of E. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that P∞ n=1(kn − 1) < ∞ and let F (T ) be nonempty, where F (T ) denotes the fixed points set of T . Let {αn}, {βn}, {γn}, {αn}, {β′ n}, {γ′ n}, {α′′ n}, {β′′ n} and {γ′′ n} be real sequen...