Meijuan Shang

Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping, but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others.

Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings

We modified the classic Mann iterative process to have strong convergence theorem for a finite family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend the results announced by many others.

A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.

THREE-STEP ITERATIONS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS

This paper introduces a three-step iteration 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 inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space. The authors show that the iterative sequence converges strongly to a common element of the two sets, which solves some variational inequality. Subsequently, the authors consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the corresponding results announced by Nakajo, Takahashi, and Toyoda.

Wiener--Hopf equations technique for general variational inequalities involving relaxed monotone mappings and nonexpansive mappings.

We show that the general variational inequalities are equivalent to the general Wiener-Hopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results improve and extend recent ones announced by many others.