Viscosity approximation method for solving variational inequality problem in real Banach spaces

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Submitted: 2024-12-06; Published: 2024-12-06

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Abstract

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 qq-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.