Viscosity approximation method for solving variational inequality problem in real Banach spaces
Keywords:Fixed Point, Hierarchical Fixed Point Problems, Strongly Accretive Mapping, Lipschitzian Mapping, Nonexpansive Mapping
In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.
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