Symmetric strong vector quasiequilibrium problems in Hausdorff locally convex spaces

• Main Authors: Cho Yeol, Chen Bin, Huang Nan-jing
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Journal of Inequalities and Applications
• Subjects: symmetric strong vector quasiequilibrium problem; Kakutani-Fan-Glicksberg fixed point theorem; closedness
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2011/1/56

<p>Abstract</p> <p>In this article, a new symmetric strong vector quasiequilibrium problem in real locally convex Hausdorff topological vector spaces is introduced and studied. An existence theorem of solutions for the symmetric strong vector quasiequilibrium problem by using Kakutani-Fan-Glicksberg fixed point theorem is obtained. Moreover, the closedness of the solution set for this problem is derived. The results presented in this article improve and extend some known results according to Long et al. [Math. Comput. Model. <b>47</b>, 445-451 (2008)], Somyot and Kanokwan [Fixed Point Theory Appl. doi:10.1155/2011/475121], and Wang et al. [Bull. Malays. Math. Sci. Soc. <url>http://www.emis.de/journals/BMMSS/pdf/acceptedpapers/2009-11-022_R1.pdf</url>].</p> <p> <b>2000 MSC: </b>49J40; 90C29.</p>