GENERAL VISCOSITY ITERATIVE PROCESS FOR SOLVING VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS INVOLVING MULTIVALUED QUASI-NONEXPANSIVE AND DEMICONTRACTIVE OPERATORS WITH APPLICATION

In this paper, we introduce and study a new iterative method which is based on viscosity general algorithm and forward-backward splitting method for finding a common element of the set of common fixed points of multivalued demicontractive and quasinonexpansive mappings and the set of solutions of variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings in real Hilbert spaces. We prove that the sequence fxng which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, our theorems are applied to approximate a common solution of fixed point problems with set-valued operators and the composite convex minimization problem. Our theorems are significant improvements on several important recent results.