A modified Popov’s subgradient extragradient method for variational inequalities in Banach spaces

Abstract

In this paper, we propose a new modification of Popov’s subgradient extragradient method for solving the variational inequality problem involving pseudo-monotone and Lipschitz-continuous mappings in the framework of Banach spaces. The weak convergence theorem of the proposed method is established without the knowledge of the Lipschitz constant of the Lipschitz continuous mapping. Finally, we provide several numerical experiments of the proposed method including comparisons with other related methods. Our result generalizes and extends many related results in the literature from Hilbert spaces to Banach spaces.