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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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  • Yekini Shehu

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. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Yekini Shehu, 2012. "A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces," Journal of Global Optimization, Springer, vol. 54(3), pages 519-535, November.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:519-535
    DOI: 10.1007/s10898-011-9775-1
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