Strong convergence of the modified hybrid steepest-descent methods for general variational inequalities

In this paper, we consider the general variational inequality GVI(F, g, C), whereF andg are mappings from a Hilbert space into itself andC is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type methodu _n+1=(1?α+θ _n+1)Tu _n +αu _n ?θ _n+1 g (Tu _n )?λ _n+1 μF(Tu _n ),n≥0. for solving the general variational inequalities. The sequencex _n is shown to converge in norm to the solutions of the general variational inequality GVI(F, g, C) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Results proved in the paper can be viewed as an refinement and improvement of previously known results.