Some Studies On Quasi Variational Inclusions And The Fixed Point Problems Of Generalized Mixed Equilibrium

This contribution first presents a strong convergent theorem for quasi variational inclusion problems with multi-valued maximal monotone mapping and inver-strongly monotone mapping and fixed point problems with nonexpansive mappings in Hilbert spaces, which extends and improves the main result of Zhang Shisheng et al.. Then some strong convergent theorems for finding the common element of the set of solutions for a generalized mixed equilibrium problem and fixed points of infinite family of hemi-relatively nonexpansive mappings are proved in a Banach space by using the CQ method and the shrinking Projection method, which extend and improve the main results of Takahashi and Zembayashi. Moreover, the method of proof adopted in the paper is different from that of them.