Abstract
In this paper, we consider the general variational inequality GVI(F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We suggest and analyze a new modified hybrid steepest-descent method of type method un+1 = (1 - α + θn+1)Tun + αun - θn+1g(Tun) - λn+1µF(Tun), n ≥ 0. for solving the general variational inequalities. The sequence {xn} 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.
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