JNCA: Weak convergence theorems for a countable family of relatively nonexpansive mappings



	Volume 10, Number 3, December 2009, pp. 407-418
Weerayuth Nilsrakoo and Satit Saejung
Key words:
Relatively nonexpansive mapping, nonexpansive mapping, variational inequality
Mathematices Subject Classification: 47H09, 47H10


	Abstract:
	In this paper, we establish weak convergence theorems for finding common fixed points of a countable family of relatively nonexpansive mappings in a uniformly smooth and uniformly convex Banach space. Weak convergence theorems for finding a common element of the set of fixed points and the set of solutions of a variational inequality problem are also obtained. With an appropriate setting, the corresponding results due to Nadezhkina--Takahashi [13] are deduced.

Weak convergence theorems for a countable family of relatively nonexpansive mappings