Weak Convergence of Iterations for Nonexpansive Mappings
Mengistu Goa Sangago · International journal of mathematics and computation · 2010
The main purpose of this paper is to prove weak convergence of a new implicit iterative algorithms for a nonexpansive mappings in a uniformly convex Banach space which satises Opial's condition by asssuming mild control conditions on the parameters. Moreover, strong convergence is obtained by imposing the semi-compactness condition on the mapping. The results presented in the paper improve and generalize results by Opial(1967), Reich(1979), and Xu and Ori (2001).