Common solutions for a monotone variational inequality problem and an infinite family of inverse strongly monotone non-self operators

In this paper, we introduce regularization methods for finding a point, being not only solution monotone variational inequality problem but also common zero an infinite family of inverse strongly non-self operators closed convex subset in real Hilbert space. these methods, finite number the is used at each iteration step. Applications to fixed point strictly pseudo-contractive and split feasibility problems are considered. As particular case, extragradient iterative method without prior knowledge operator norms solving (SFP) obtained. Numerical examples given illustration.