厚芝 幸子

In this paper, we study Halpern's type iterations [11] for nonexpansive semigroups and prove strong convergence to common attractive points of uniformly asymptotically left regular nonexpansive semigroups in Hilbert spaces. Using this result, we obtain some strong convergence theorems in Hilbert spaces.

In this paper, we introduce the concept of common attractive points of a nonexpansive semigroup in a Hilbert space and study fundamental properties for the points. We also prove a nonlinear mean convergence theorem of Baillon's type [3] without convexity for nonexpansive semigroups. Using this result, we obtain new and well-known nonlinear mean convergence theorems in a Hilbert space.

We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a beta-inverse-strongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesaro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang (2009), Peng and Yao (2009), Shimizu and Takahashi (1997), and some authors.