Fixed Point Theorems And Iterative Convergence For Generalized Variational Inequalities And Mixed Equilibrium Problems

In this paper,first,two kinds of fixed point theorems are studied in fuzzy metric space,which includes common fixed point theorems for a class of contractive mapping of integral type and common fixed point theorem for a new class of Altman type mapping involving four mappings.Next,the convergence problems of the iterative sequences of fixed points for multi-valued mappings of the monotone type and multi-valued strongly pseudo-contractive mappings are studied.By using a new analytical method,the strong convergence theorems of the Ishikawa iterative sequences with mixed errors of fixed points for multi-valued mappings of the monotone type and multi-valued strongly pseudo-contractive mappings are established without any boundedness.Final,we introduce the new viscosity Cesàro mean iterative algorithms and establish the strong convergence theorem of common element of the set of fixed points for nonexpansive semigroups and the set of solutions for generalized variational inequalities and mixed equilibrium problems in Hilbert spaces by using the viscosity iterative algorithms.Therefore,the results in this paper extend and improve the corresponding results of some reference.