Viscosity method for hierarchical variational inequalities and variational inclusions on Hadamard manifolds

Doaa Filali, Mohammad Dilshad*, Mohammad Akram, Feeroz Babu, Izhar Ahmad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This article aims to introduce and analyze the viscosity method for hierarchical variational inequalities involving a ϕ-contraction mapping defined over a common solution set of variational inclusion and fixed points of a nonexpansive mapping on Hadamard manifolds. Several consequences of the composed method and its convergence theorem are presented. The convergence results of this article generalize and extend some existing results from Hilbert/Banach spaces and from Hadamard manifolds. We also present an application to a nonsmooth optimization problem. Finally, we clarify the convergence analysis of the proposed method by some computational numerical experiments in Hadamard manifold.

Original languageEnglish
Article number66
JournalJournal of Inequalities and Applications
Issue number1
StatePublished - 2021

Bibliographical note

Funding Information:
This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program. The authors sincerely thank the unknown referees for their valuable suggestions and useful comments that have led to the present form of the original manuscript.

Publisher Copyright:
© 2021, The Author(s).


  • Fixed point problem
  • Hadamard manifold
  • Hierarchical variational inquality
  • Nonexpansive mapping
  • Variational inclusion problem
  • Viscosity method
  • ϕ-contraction mapping

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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