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 - Team, Support (Thai Journal of Mathematics, 2014)
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. CTL2012, Chen C2012 and Yao et al. 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.