A Modified Halpern-Type Iteration for Bregman Relatively Nonexpansive Mappings

A Modified Halpern-type Iteration Process for an Equilibrium Problem and a Family of Relatively Quasi-nonexpansive Mappings in Banach Spaces

In this paper, based on a generalized projection, we introduce a new modified Halpern-type iteration algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of a common fixed point of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We establish the strong convergence theorem and obtain some ...

Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces

We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpa...

Modified Halpern Iteration of Asymptotically Non-Expansive Mappings

Convergence and Stability of Modified Random SP-Iteration for A Generalized Asymptotically Quasi-Nonexpansive Mappings

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications

In this paper, we show strong convergence theorems of modified Ishikawa iteration with errors and modified Halpern iteration with error for relatively nonexpansive mappings in a Banach space. The results extend and improve the corresponding results of Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others. Mathematics Subject Classification: 47H09; 47H10