Iterative algorithm of solutions for a system of generalized mixed implicity equilibrium problems in reflexive Banach spaces (Q426507)

A mixed equilibrium problem includes variational inequalities and optimization problems as well as problems of Nash equilibria, saddle-point problems, fixed-point problems and complementary problems as special cases. Various kinds of iterative algorithms for solving the equilibrium problems have been developed by many authors.NEWLINENEWLINE In this paper, a new system of generalized mixed implicite equilibrium problems involving non-monotone set-valued mappings with non-compact values in real refexive Banach spaces are studied. A system of generalized equation problems is considered and its equivalence with the system of generalized mixed implicite equilibrium problems is shown. Using a fixed-point formulation of the system of generalized equations problems, a new iterative algorithm for solving the system of generalized mixed implicite equilibrium problems is developed. Under certain assumptions the strong convergence of the iterative sequences generated by the algorithm is proved.