A Strong Convergence Theorem for a Family of Quasi--Nonexpansive Mappings in a Banach Space

A Strong Convergence Theorem for [-1pt] a Family of Quasi--Nonexpansive Mappings in [-1pt] a Banach Space

The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property K . The results of this paper improve and extend the results of S. Matsushita and W. Takahashi 2005 ...

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

Strong Convergence of the Iterations of Quasi $phi$-nonexpansive Mappings and its Applications in Banach Spaces

In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings.  Then, we give  applications of our main results in equilibrium problems.

Strong Convergence Theorems for Nonexpansive Mappings and Inverse-strongly-monotone Mappings in a Banach Space

In this paper, we introduce a new iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common el...

Weak and Strong Convergence Theorems for Finite Family of Nonself Asymptotically Nonexpansive Mappings in Banach Space

In this paper, several weak and strong convergence theorems are established for a new modified iterations with errors for finite family of nonself asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type and Noor-type iterations are covered by the new iteration scheme. Our convergence theorems improve, unify and generalize many important results in the current literatures.