Viscosity Approximation Methods for * −Nonexpansive Multi-Valued Mappings in Convex Metric Spaces

In this paper, we prove convergence theorems for viscosity approximation processes involving * −nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points of them. Our results improve and extend some corresponding results.

Viscosity Approximation Methods for a General Variational Inequality System and Fixed Point Problems in Banach Spaces

In Banach spaces, we study the problem of solving a more general variational inequality system for an asymptotically non-expansive mapping. We give a new viscosity approximation scheme to find a common element. Some strong convergence theorems of the proposed iterative method are obtained. A numerical experiment is given to show the implementation and efficiency of our main theorem. Our results presented in this paper generalize and complement many recent ones.

Convergence Theorems of Variational Inequality for Asymptotically Nonexpansive Nonself Mapping in CAT(0) Spaces

The aim of this manuscript is to get the strong convergence theorems of the Moudafi’s viscosity approximation methods for an asymptotically nonexpansive nonself mapping in C A T ( 0 ) spaces.

Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

An algorithm is introduced to find an answer to both inclusion problems and fixed point problems. This algorithm is a modification of Tseng type methods inspired by Mann’s type iteration and viscosity approximation methods. On certain conditions, the iteration obtained from the algorithm converges strongly. Moreover, applications to the convex feasibility problem and the signal recovery in compressed sensing are considered. Especially, some numerical experiments of the algorithm are demonstrated. These results are compared to those of the previous algorithm.