Existence results for generalized vector equilibrium problems with applications.pdfVIP

Appl. Math. Mech. -Engl. Ed., 35(7), 913–924 (2014) Applied Mathematics DOI 10.1007/s10483-014-1867-9 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 (English Edition) Existence results for generalized vector equilibrium problems with applications∗ 1 2 Ming-ge YANG ( ) , Nan-jing HUANG () (1. Department of Mathematics, Luoyang Normal University, Luoyang 471022, Henan Province, P. R. China; 2. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China) Abstract By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature. Key words generalized vector equilibrium problem, generalized semi-infinite program, abstract convex space, RC-map Chinese Library Classification O224, O177 2010 Mathematics Subject Classification 91B50, 90C34, 54H25 1 Introduction Let R = (−∞, +∞) and A be a nonempty subset of a topological vector space E . Assume that f : A ×A → R is a function such that f (x, x) 0 for all x ∈ A. The scalar equilibrium problem considered by Blum and Oettli[1] is to find x0 ∈A such that f (x0 , y) 0 for all y ∈A. This scalar equilibrium problem includes some fundamental mathematical pro