Abstract
In this paper, we introduce a system of generalized nonlinear mixed variational inequalities and obtain the approximate solvability by using the resolvent parallel technique. Our results may be viewed as an extension and improvement of the previously known results for variational inequalities.
Highlights
Introduction and preliminariesVariational inequality theory, which was introduced by Stampacchia [ ] in, has been witnessed as an interesting branch of mathematical and engineering sciences with a wide range of applications in industry, finance, economics and pure and applied sciences
Inspired and motivated by research in this area, we introduce a system of generalized nonlinear mixed variational inequalities problem involving two different nonlinear operators
It is well known that if the nonlinear term in the mixed variational inequality is a proper, convex, and lower semicontinuous, one can establish the equivalence between the mixed variational inequality and the fixed point problem
Summary
Introduction and preliminariesVariational inequality theory, which was introduced by Stampacchia [ ] in , has been witnessed as an interesting branch of mathematical and engineering sciences with a wide range of applications in industry, finance, economics and pure and applied sciences. This alternative equivalence has been used to develop several projection iterative methods for solving variational inequalities and related optimization problems. Several extensions and generalizations of the system of strongly monotonic variational inequalities have been considered by many authors [ – ].
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