Set-Valued Resolvent Equations and Mixed Variational Inequalities |
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Authors: | Muhammad Aslam Noor Khalida Inayat Noor ThM Rassias |
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Institution: | aDepartment of Mathematics, College of Science, P.O. Box 2455, King Saud University, Riyadh, 11451, Saudi Arabia;bDepartment of Mathematics, National Technical University of Athens, Zografou Campus, 15 773, Athens, Greece |
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Abstract: | In this paper, we introduce and study a new class of variational inequalities, which is called the generalized set-valued mixed variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed point problems, and the generalized set-valued resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area. |
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