THE SYSTEMS OF CONDENSING OPERATOR EQUATIONS AND THE SYSTEMS OF VARIATIONAL INEQUALITIES WITH THE CONDENSING OPERATORS AND APPLICATION TO THE SYSTEM OF INTEGRAL EQUATIONS

The purpose of this paper is to prove some existence theorems for solutions of a certain system of multivariate condensing operator equations and a certain system of variational inequalities with multivariate condensing operators. The main results are applied to prove the multivariate best proximity point theorems for multivariate condensing operators and the existence theorems of solutions for a kind of the mixed type system of nonlinear integral equations. To get the expected results, a comprehensive analytical method was used. The results of this article improve and extend the previous classical results given in the literature.