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

Author(s)

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

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.

DOI: 10.52737/18291163-2021.13.3-1-20 Armenian Journal of Mathematics, 13(3) 1-20

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Keywords

Fixed Point, Hierarchical Fixed Point Problems, Strongly Accretive Mapping, Lipschitzian Mapping, Nonexpansive Mapping

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