Viscosity iteration method for variational inclusions, equilibria and fixed points on Hadamard manifolds
Journal of Decision Making and Healthcare, Volume 2, Issue 1, April 2025, Pages: 64–82
LU-CHUAN CENG
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
YUE ZENG
Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA
XIAOPENG ZHAO
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Abstract
In this paper, we first introduce a viscosity iteration method for finding a common solution of a countable family of quasi-variational inclusion problems, an equilibrium problem (for short, EP) and a fixed-point problem of a nonexpansive mapping on Hadamard manifolds. Then, under some mild conditions, we prove that the iterative sequence generated by the suggested algorithm converges to a common solution. As applications, we utilize our main result to deal with the minimization problem with EP constraint and the variational inequality problem with EP constraint on Hadamard manifolds, respectively.
Cite this Article as
Lu-Chuan Ceng, Yue Zeng, and Xiaopeng Zhao, Viscosity iteration method for variational inclusions, equilibria and fixed points on Hadamard manifolds, Journal of Decision Making and Healthcare, 2(1), 64–82, 2025