In this paper, we consider a new class of variational inequalities, which is called the harmonic variational inequality. It is shown that that the minimum of a differentiable harmonic convex function on the harmonic convex set can be characterized by the harmonic variational inequality. We use the auxiliary principle technique to discuss the existence of a solution of the harmonic variational inequality. Results proved in this paper may stimulate further research in this field.
Digital Object Identifier (DOI)
Aslam Noor, Muhammad and Inayat Noor, Khalida
"Harmonic Variational Inequalities,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 22.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss5/22