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

Yekini Shehu ()

Journal of Global Optimization, 2012, vol. 54, issue 3, 519-535

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

Keywords: Relatively nonexpansive mappings; Generalized projection operator; Equilibrium problem; Banach spaces; 47H06; 47H09; 47J05; 47J25 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10898-011-9775-1

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