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.