Weak and Strong Convergence Theorems for Approximating Common Fixed Points of Three Nonexpansive Mappings

P. Glubudom

Abstract

In this paper, a new three-step iterative scheme for three nonexpansive mappings is introduced and studied. Weak and strong convergence theorems of such iterations to a common fixed point of the nonexpansive mappings are established. The results obtained in this paper extend and improve the results due to [W. Takahashi and T. Tamura, convergence theorems for a pair of nonexpansive mappings, J. Convex Anal., 5 (1995), 45–58], [K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301–308] and [H. F. Senter and W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 44 (1974), 375–380] and [G. Liu, D. Lei and S. Li, Approximating fixed points of nonexpansive mappings, Internat. J. Math. & Math. Sci., 24 (2000), 173–177].