Extragradient method for solving variational inequalities and fixed point problems

Sunny generalized nonexpansive retraction is different from the metric projection in Hilbert spaces and generalized metric projection in Banach spaces. In this paper, replacing metric projections by the sunny generalized nonexpansive retraction, we propose the new algorithm for an $\alpha$-inverse-strongly monotone operator and a generalized nonexpansive mapping in Banach spaces. We present a strong convergence theorem by this method under suitable conditions.