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

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  • S. Saewan

  • P. Kumam

Abstract

The purpose of this paper is to present new hybrid Ishikawa iteration process by the generalized f-projection operator for finding a common element of the fixed point set for two countable families of weak relatively nonexpansive mappings and the set of solutions of the system of generalized Ky Fan inequalities in a uniformly convex and uniformly smooth Banach space. Furthermore, we show that our new iterative scheme converges strongly to a common element of the afore mentioned sets. As applications, we apply our results to obtain some new results for finding a solution of a common fixed point of two countable in finite families, a system of generalized Ky Fan inequalities and a common zero-point problem for general B-monotone and maximal monotone operators in Banach spaces. The results presented in this paper improve and extend important recent results. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • S. Saewan & P. Kumam, 2013. "A generalized f-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities," Journal of Global Optimization, Springer, vol. 56(2), pages 623-645, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:623-645
    DOI: 10.1007/s10898-012-9922-3
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    References listed on IDEAS

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    1. Prasit Cholamjiak & Suthep Suantai, 2010. "Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi‐Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Cited by:

    1. Jeong, Jae Ug & Kim, Soo Hwan, 2015. "An iterative method for total quasi-ϕ-asymptotically nonexpansive semi-groups and generalized mixed equilibrium problems in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 39-48.

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