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Weak Convergence of Iterations for Nonexpansive Mappings

Mengistu Goa Sangago

Abstract


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).

Keywords


uniform convexity, nonexpansive mapping, weak convergence, demi-closed mapping, Opial's condition

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