A New Hybrid Iterative Scheme for Countable Families of Relatively Quasi-Nonexpansive Mappings and System of Equilibrium Problems

Yekini Shehu

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-23

Abstract:

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasi-nonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized -projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:131890

DOI: 10.1155/2011/131890

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