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A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces

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Abstract

In this paper, we construct a new iterative scheme and prove strong convergence theorem for approximation of a common fixed point of a countable family of relatively nonexpansive mappings, which is also a solution to an equilibrium problem 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 an equilibrium problem in a real Hilbert space and prove strong convergence of general H-monotone 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. Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

    Yekini Shehu

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  1. Yekini Shehu
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Shehu, Y. A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces. J Glob Optim 54, 519–535 (2012). https://doi.org/10.1007/s10898-011-9775-1

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  • DOI: https://doi.org/10.1007/s10898-011-9775-1

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