Affiliation:
1. Department of Industrial Engineering and Management University of Medicine, Pharmacy, Science and Technology “George Emil Palade” Tg . Mureş Romania
Abstract
Abstract
It was claimed in [Sadeqi, I.—Salehi Paydar, M.: A comparative study of Ky Fan hemicontinuity and Brezis pseudomonotonicity of mappings and existence results, J. Optim. Theory Appl. 165(2) (2015), 344–358] that the gradient of a convex Gâteaux differentiable function is Fanhemicontinuous. The aim of the present paper is to correct this implication by exemplifying for
∇
‖
⋅
‖
$\nabla \|\cdot \|$
in a Hilbert space. This goal was achieved by considering its domain to be scalarly-positive (see Definition 3). For a perturbation of a Fan-hemicontinuous operator with
∇
‖
⋅
‖
,
$\nabla \|\cdot \|,$
weak compactness for the set of solutions of the variational inequality problem is obtained.