General Viscosity Iterative Process for Solving Variational Inclusion and Fixed Point Problems Involving Multi-Valued Quasi-Non-Expansive 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 quasi-nonexpansive 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 $x_n$ 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.

کلیدواژه ها:

Common fixed points ، Variational inclusion problems ، Set-valued operators ، Iterative methods