A generalized f-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities

Authors:
S. Saewan;P. Kumam
Affiliations:
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Thrungkru, Bangkok, Thailand 10140;Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Thrungkru, Bangkok, Thailand 10140
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

The purpose of this paper is to present new hybrid Ishikawaiteration process by the generalized f-projection operator forfinding a common element of the fixed point set for two countablefamilies of weak relatively nonexpansive mappings and the set ofsolutions of the system of generalized Ky Fan inequalities in auniformly convex and uniformly smooth Banach space. Furthermore, weshow that our new iterative scheme converges strongly to a commonelement of the afore mentioned sets. As applications, we apply ourresults to obtain some new results for finding a solution of acommon fixed point of two countable in finite families, a system ofgeneralized Ky Fan inequalities and a common zero-point problem forgeneral B-monotone and maximal monotone operators in Banachspaces. The results presented in this paper improve and extendimportant recent results.