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Zbl 1228.65104
Noor, Muhammad Aslam; Ullah, Saleem; Noor, Khalida Inayat; Al-Said, Eisa
Iterative methods for solving extended general mixed variational inequalities. (English)
[J] Comput. Math. Appl. 62, No. 2, 804-813 (2011). ISSN 0898-1221

Summary: 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.

MSC 2000:: *65K15
47J20 Inequalities involving nonlinear operators
47J25 Methods for solving nonlinear operator equations (general)
49J40 Variational methods including variational inequalities
90C33 Complementarity problems

Keywords: variational inequalities; nonconvex functions; fixed point problem; resolvent operator; resolvent equations; projection operator; convergence; dynamical systems

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Zentralblatt MATH Berlin [Germany]