Regularization extragradient method for Lipschitz continuous mappings and inverse strongly-monotone mappings in Hilbert spaces

The purpose of this paper is to present a regularization variant of the extragradient method for finding a common element of the solution sets for a variational inequality problem involving a $$ \tilde k $$ -Lipschitz continuous monotone mapping A and for a finite family of λ i -inverse strongly-monotone operators {A i } = 1 from a closed convex subset K into the Hilbert space H.