New results on system of variational inequalities and fixed point theorem

Abstract

In (Croat. Oper. Res. Rev, 13(1), 131-135, (2022).) A. Benhadid showed by a counterexample that a number of publications in the research on the variational inequalities system contains inaccurate results about applying the Lipschitz continuity concept in relation to both the first and second variables during the proof of the main theorem on the part of authors. In this paper, We suggest to applying fixed point theorem to correct the main results of some publications.

Keywords

• fixed point problem
• relaxed (e1, e2)-cocoercive mappings
• variational inequalities system’s with nonlinear mappings