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

Journal of inequalities and applications

Feeroz Babu¹  Doaa Filali²  Izhar Ahmad³  Mohammad Akram⁴  Mohammad Dilshad⁵ 

[1] Department of Applied Mathematics, Aligarh Muslim University, Aligarh, India;Department of Mathematical Science, Collage of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, Kingdom of Saudi Arabia;Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Kingdom of Saudi Arabia;Department of Mathematics, Islamic University of Madinah, 170, Madinah, Kingdom of Saudi Arabia;Department of Mathematics, University of Tabuk, 71491, Tabuk, Kingdom of Saudi Arabia;

关键词: Viscosity method;    Hierarchical variational inquality;    Variational inclusion problem;    Fixed point problem;    Nonexpansive mapping;    ϕ;    Hadamard manifold;    47J53;    47J22;    47J25;    49J40;   

DOI  :  10.1186/s13660-021-02598-8

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY