A VISCOSITY NONLINEAR MIDPOINT ALGORITHM FOR NONEXPANSIVE SEMIGROUP

Abstract

In this paper, we proposed a viscosity nonlinear midpoint algorithm (VNMA) for finding a solution of  fixed point problem for a nonexpansive semigroup in real Hilbert spaces. Under certain conditions control on parameters, the iteration sequences generated by the proposed algorithms are proved to be strongly convergent to a solution of fixed point problem for a nonexpansive semigroup. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.