Author(s)

Hongbo Liu, Yi Li

School of Science, Southwest University of Science and Technology, Mianyang, China.

Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

Hybrid Iterative Algorithm, Uniformly Asymptotically Nonexpansive Semigroups, Equilibrium Problem, Common Fixed Point

Liu, H. and Li, Y. (2014) Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups. Advances in Pure Mathematics, 4, 244-252. doi: 10.4236/apm.2014.46033.