tailieunhanh - Báo cáo hóa học: "GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS WITH SET-VALUED MAPPINGS"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS WITH SET-VALUED MAPPINGS | GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS WITH SET-VALUED MAPpINGS JIAN WEN PENG AND DAO LI ZHU Received 26 October 2005 Revised 5 March 2006 Accepted 12 April 2006 A new mathematical model of generalized vector quasiequilibrium problem with setvalued mappings is introduced and several existence results of a solution for the generalized vector quasiequilibrium problem with and without O-condensing mapping are shown. The results in this paper extend and unify those results in the literature. Copyright 2006 J. W. Peng and D. L. Zhu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Throughout this paper let Z E and F be topological vector spaces let X Q E and Y Q F be nonempty closed and convex subsets. Let D X 2X T X 2y and V X X Y X X 2Z be set-valued mappings and let C X 2Z be a set-valued mapping such that C x is a closed pointed and convex cone with int C x 0 for each x E X where int C x denotes the interior of the set C x . Then the generalized vector quasi-equilibrium problem with set-valued mappings GVQEP is to find x y in X X Y such that x E D x y E T x V x y z - int C x z E D x . The GVQEP is a new interesting meaningful and general mathematical model which contains many mathematical models as special cases for some examples we have the following. i If V is replaced by a single-valued function f X X Y X X Z and C x C for all x E X then the GVQEP reduces to finding x y in X X Y such that x E D x y E T x f x y z E intC z E D x . It was investigated by Chiang et al. in 7 . Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 69252 Pages 1-12 DOI JIA 2006 69252 2 Generalized vector quasi-equilibrium problem If V is replaced by a scalar function f X X Y X X R and C x r e R r 0 for all x e X then the GVQEP reduces to finding x y