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Báo cáo hóa học: " Research Article Existence Result of Generalized Vector Quasiequilibrium Problems in Locally G-Convex Spaces"

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: Research Article Existence Result of Generalized Vector Quasiequilibrium Problems in Locally G-Convex Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 967515 13 pages doi 10.1155 2011 967515 Research Article Existence Result of Generalized Vector Quasiequilibrium Problems in Locally G-ConVex Spaces Somyot Plubtieng and Kanokwan Sitthithakerngkiet Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Somyot Plubtieng somyotp@nu.ac.th Received 30 November 2010 Accepted 18 February 2011 Academic Editor Yeol J. Cho Copyright 2011 S. Plubtieng and K. Sitthithakerngkiet. 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. This paper deals with the generalized strong vector quasiequilibrium problems without convexity in locally G-convex spaces. Using the Kakutani-Fan-Glicksberg fixed point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values the existence theorems for them are established. Moreover we also discuss the closedness of strong solution set for the generalized strong vector quasiequilibrium problems. 1. Introduction Let X be real topological vector space and let C be a nonempty closed convex subset of X. Let F C X C R be a bifunction where R is the set of real numbers. The equilibrium problem for F is to find x e C such that F x y 0 Vy e C. 1.1 Problem 1.1 was studied by Blum and Oettli 1 . The set of solution of 1.1 is denoted by EP F . The equilibrium problem contains many important problems as special cases including optimization Nash equilibrium complementarity and fixed point problems see 1-3 and the references therein . Recently there has been an increasing interest in the study of vector equilibrium problems. Many results on the existence of solutions for vector variational inequalities and vector equilibrium problems have been established see e.g.