Isaac Scientific Publishing

Advances in Analysis

Fixed Point Approximations with Finite Relatively Nonexpansive Maps in Some Real Banach Spaces

Download PDF (560.3 KB) PP. 19 - 29 Pub. Date: January 15, 2017

DOI: 10.22606/aan.2017.11004

Author(s)

  • Umar Yusuf Batsari*
    Department of Mathematics and Statistics, Hassan Usman Katsina Polytechnic, Katsina State, Nigeria

Abstract

Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. In this paper, it is shown that {xn} obtained from Batsari’s[21] CQ algorithm with relatively nonexpansive maps converges strongly to a point bx which is also a common fixed point x of some finite relatively nonexpansive mappings and solves a system of equilibrium problems in E. The result obtained improves some existing results in the literature.

Keywords

Relatively nonexpansive mappings; equilibrium problems; uniformly smooth space; uniformly convex space; bounded sequence.

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