Iterative Approximations Of Fixed Points For Several Classes Of Nonlinear Semigroups

In this paper,first we introduce and study asymptotically pseudocontractive type semigroups and implicit iterative sequence,and prove the strong convergence theorem of implicit iterative sequence of common fixed points for asymptotically pseudocontractive type semigroups in Banach space,which extend the corresponding results in some references to the case of asymptotically pseudocontractive type semigroups.Next,we introduce and study new implicit iterative sequence for strictly pseudocontractive semigroups and establish the weak convergence theorems of implicit iterative sequence of common fixed points for strictly pseudocontractive semigroups in Banach spaces.Finall,we introduce and study of more general implicit and explicit viscosity iterative algorithms for nonexpansive semigroups and establish the strong convergence theorems of viscosity approximation method for implicit and explicit iterative algorithms to find a common element of the set of common fixed points for nonexpansive semigroups and the set of solutions of variational inequality with a strongly monotone mapping in Hilbert spaces,which extend and improve the corresponding results in some references.