Three-Step Fixed Point Iteration for Multivalued Mapping in Banach Spaces

New three-step iteration process and fixed point approximation in Banach spaces

‎In this paper we propose a new iteration process‎, ‎called the $K^{ast }$ iteration process‎, ‎for approximation of fixed‎ ‎points‎. ‎We show that our iteration process is faster than the existing well-known iteration processes using numerical examples‎. ‎Stability of the $K^{ast‎}‎$ iteration process is also discussed‎. ‎Finally we prove some weak and strong convergence theorems for Suzuki ge...

Three-step Fixed Point Iteration for Multivalued Mapping with Errors in Banach Spaces

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping with errors, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results.

Common fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces

Let X be a Banach space and K a nonempty subset of X. The set K is called proximinal if for each x ∈ X, there exists an element y ∈ K such that ‖x − y‖ d x,K , where d x,K inf{‖x − z‖ : z ∈ K}. Let CB K , C K , P K , F T denote the family of nonempty closed bounded subsets, nonempty compact subsets, nonempty proximinal bounded subsets of K, and the set of fixed points, respectively. A multivalu...

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces