A common minimum-norm solution of a generalized equilibrium problem and a fixed point problem for a countable family of nonexpansive mappings

Hathaikarn Wattanataweekul, Utith Inprasit, Weerayuth Nilsrakoo

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Abstract

We introduce a new iterative scheme for finding a common

minimum-norm solution of a generalized equilibrium problem and a fixed point problem for a countable family of nonexpansive mappings and then establish strong convergence theorems of the scheme by using the NST-condition. Our result extends and improves the main result of Cai et al. \cite{CTL2012}, Chen \cite{C2012} and Yao et al. \cite{YZL2009} and

many others. Finally, we apply our results to solve the problem of finding common zeros of maximal monotone operators, the common minimizer problem, the multiple-sets split feasibility problem.

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Published

2014-08-01

How to Cite

Team, S. (2014). A common minimum-norm solution of a generalized equilibrium problem and a fixed point problem for a countable family of nonexpansive mappings: Hathaikarn Wattanataweekul, Utith Inprasit, Weerayuth Nilsrakoo. Thai Journal of Mathematics, 12(2), 397–430. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/460

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