Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

H. A. Abass*, O. K. Oyewole, L. O. Jolaoso, K. O. Aremu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this article, we introduce a forward–backward splitting method with a new step size rule for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multi-valued vector field on a Hadamard manifold. Using a Mann, viscosity and an inertial extrapolation method, we establish a convergence result without prior knowledge of the Lipschitz constant of the underlying operator. We present some applications of our result to variational inequality problem. Finally, we present some numerical examples to demonstrate the numerical behavior of our proposed method. The result discuss in this article extends and complements many related results in the literature.

Original languageEnglish
Pages (from-to)1604-1627
Number of pages24
JournalApplicable Analysis
Volume103
Issue number9
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • Hadamard manifold
  • Riemannian manifold
  • Variational inclusion problem
  • inertial Tseng method
  • monotone operator

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