Nonlinear Viscosity Algorithm with Perturbation for Nonexpansive Multi-Valued Mappings

In this paper, based on viscosity technique with perturbation, we introduce a new non-linear viscosity algorithm for finding a element of the set of fixed points of nonexpansivemulti-valued mappings in a Hilbert space. We derive a strong convergence theorem for thisnew algorithm under appropriate assumptions. Moreover, in support of our results, somenumerical examples (using Matlab software) are also presented.

Keywords:

Nonexpansive multi-valed , strongly positive linear bounded operator , xed point , Hilbert space