Fixed Point Theorem For A Class Of Mapping In Probabilistic Metric Spaces And Iterative Approximation Of Solutions For Variational Inequality

In this paper,first we briefly introduce the general situation of the research of fixed point theorem for a class of mapping in probabilistic metric spaces and iterative approximation of solutions for variational inequality and the work outlines of this paper Next,by using the compatible conditions of self-mapping pair in non-Archimedean Menger probabilistic metric spaces,common fixed point theorem for a class new of Altman type mapping are proved in non-Archimedean Menger probabilistic metric spaces.As an application we also discuss the existence and uniqueness of solutions for a class of functional equations arising in dynamic programming.Then,we study conve-rgence problems of viscosity parallel iterative algorithm for nearly uniformly Lipschitz mapping in normed linear spaces.Strong convergence theorem of viscosity parallel iterative algorithm with mixed errors of fixed point for nearly uniformly Lipschitz generalized asymptotically demicontractive mappings in normed linear spaces is established under weaker conditions.Final,we introduce the new viscosity iterative algorithms and establish the strong convergence theorem of viscosity iterative algorith-ms to find a common element of the set of fixed points for nonexpansive semigroups and the set of solutions of generalized variational inequalities in Hilbert spaces.Theref-ore,the results in this paper extend and improve the corresponding results of some reference.