Iterative methods for solving extended general mixed variational inequalities

Authors:
Muhammad Aslam Noor;Saleem Ullah;Khalida Inayat Noor;Eisa Al-Said
Affiliations:
Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan and Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia;Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan;Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan;Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, we introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.