Triple Mann Iteration Method for Variational Inclusions, Equilibria, and Common Fixed Points of Finitely Many Quasi-Nonexpansive Mappings on Hadamard Manifolds

Abstract

In this paper, we introduce a triple Mann iteration method for approximating an element in the set of common solutions of a system of quasivariational inclusion issues, which is an equilibrium problem and a common fixed point problem (CFPP) of finitely many quasi-nonexpansive operators on a Hadamard manifold. Through some suitable assumptions, we prove that the sequence constructed in the suggested algorithm is convergent to an element in the set of common solutions. Finally, making use of the main result, we deal with the minimizing problem with a CFPP constraint and saddle point problem with a CFPP constraint on a Hadamard manifold, respectively.

Keywords

• triple Mann iteration method
• quasivariational inclusion issue
• equilibrium problem
• maximal monotone vector field
• quasi-nonexpansive mapping
• Hadamard’s manifold