Sunny generalized nonexpansive retraction and convergence theorems by extragradient method in Banach spaces
Zeynab Jouymandi, Fridoun Moradlou · arXiv (Cornell University) · 2015
Sunny generalized nonexpansive retraction is different from the metric projection and sunny nonexpansive retraction in Banach spaces. In this paper, using sunny generalized nonexpansive retraction, we propose a new extragradient method for finding a common element of the set of solutions of a generalized equilibrium problem and variational inequality for an $\alpha$-inverse-strongly monotone operator and fixed points of two relatively nonexpansive mappings in Banach spaces. We prove strong convergence theorems by this method under suitable conditions. An numerical example is given to illustrate the usability of our results.