Iterative Convergences Of Fixed Points For Several Classes Of Nonlinear Mappings And Solutions For Variational Inequalities

In this paper,first we study convergence of Reich-Takahashi iterative sequences for asymptotically nonexpansive type mapping in a real Banach space with a uniformly Gateaux differentiable norm and establish strong convergence theorems of ReichTakahashi iterative sequences for asymptotically nonexpansive type mapping.Next,under the weaker condition,we study the problems of the iterative approximation of the sequence defined by the steepest descent method of zero points for strongly accretive mappings in normed linear space by using a new analytical method.Then,we introduce and study a class of system of variational inequalities with set value mappings and iterative algorithm in Hilbert spaces.The strong convergence theorem of the iterative algorithm of the solution for the variational inequalities with set value mappings is established by using the resolvent operator technique,and a convergence rate estimate formula is also given in our results.Finally,we introduce more general viscosity iterative algorithm for nonexpansive mapping and establish the strong convergence theorems of viscosity approximation method for iterative sequence to find a common element of the set of fixed points for nonexpansive mapping and the set of solutions of generalized variational inequality with a strongly monotone mapping in Hilbert spaces.The results presented in this paper extend and improve the corresponding results in some references.