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Iterative approximation of countable family of relatively nonexpansive mappings and system of equilibrium problems in Banach spaces

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Abstract

Our purpose in this paper is to construct a new iterative scheme and prove strong convergence theorem using the iterative scheme for approximation of a common fixed point of a countable family of relatively nonexpansive mappings, which is also a solution to a finite system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space. We apply our results to approximate fixed point of a nonexpansive mapping, which is also solution to a finite system of equilibrium problems in a real Hilbert space, and approximate a common solution to finite system of variational inequality problems and convex minimization problems which is also a common solution to countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space. Our results extend many known recent results in the literature.

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  1. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Yekini Shehu

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  1. Yekini Shehu
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Shehu, Y. Iterative approximation of countable family of relatively nonexpansive mappings and system of equilibrium problems in Banach spaces. Afr. Mat. 26, 1049–1069 (2015). https://doi.org/10.1007/s13370-014-0265-8

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