A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces
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
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Volume (Year): 54 (2012)
Issue (Month): 3 (November)
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