Strong Convergence of Modified Iteration Processes for Relatively Weak Nonexpansive Mappings

- Journal title : Kyungpook mathematical journal
- Volume 52, Issue 4, 2012, pp.433-441
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2012.52.4.433

Title & Authors

Strong Convergence of Modified Iteration Processes for Relatively Weak Nonexpansive Mappings

Boonchari, Daruni; Saejung, Satit;

Boonchari, Daruni; Saejung, Satit;

Abstract

We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276-286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685-703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee`s convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.

Keywords

relatively nonexpansive mapping;relatively weak nonexpansive mapping;shrinking projection method;

Language

English

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