Mixed variational like inequalities involving perturbed operator

Abstract

In this paper, we study mixed variational like inequalities involving perturbed operator (in short, PMVLI) in real Hilbert spaces. Furthermore, we prove the existence of solution of PMVLI by using strongly monotonicity and Lipschitz continuity of perturbed operator, and auxiliary principle technique. Some special cases have also been discussed. Our results in this paper are new which can be considered as a significant extension and refinement of previously known results in the literature.