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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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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangmod, Thrungkru, Bangkok, 10140, Thailand

    S. Saewan & P. Kumam

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  1. S. Saewan
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  2. P. Kumam
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Correspondence to P. Kumam.

Additional information

Ms Siwaporn Saewan was supported by grant under the program Strategic Scholarships for Frontier Research Network for the Join Ph.D. Program Thai Doctoral degree from the Office of the Higher Education Commission, Thailand.

This research was partially supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission for financial support (under NRU-CSEC project no. 54000267).

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Saewan, S., Kumam, P. A generalized f-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities. J Glob Optim 56, 623–645 (2013). https://doi.org/10.1007/s10898-012-9922-3

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