DOI: 10.24193/fpt-ro.2020.2.40

Authors: S. Al-Homidan, Q.H. Ansari, F. Babu and J.-C. Yao

Abstract: In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a φ-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds.

Key Words and Phrases: Viscosity method, φ-contraction mappings, hierarchical variational inequality problem, Moreau-Yosida regularization, hierarchical minimization problem, Hadamard manifolds, monotone vector fields, geodesic convexity, nonexpansive mappings.

2010 Mathematics Subject Classification: 58E35, 58C30, 47H10, 49J53, 47J20, 47J25.

Published on-line: July 1st, 2020.

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