2014•Journal of Inequalities and ApplicationsOpen access

Convergence theorems of a new iteration for two nonexpansive mappings

Xue-Ping Hou, Hongxia Du

Abstract

The purpose of this paper is to introduce the following new general implicit iteration scheme for approximating the common fixed points of a pair of nonexpansive mappings in a uniformly convex Banach space: for any , the iterative process defined by , , where , , , , , , are seven sequences of real numbers satisfying , , and are two nonexpansive mappings. We approximate the common fixed points of these two mappings by weak and strong convergence of the scheme.

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Key concepts: Mathematics, Banach space, Convergence (economics), Fixed point, Regular polygon, Scheme (mathematics), Iterative and incremental development, Applied mathematics