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 A Hilbert-Type Integral Inequality in the Whole Plane with the Homogeneous Kernel of Degree −2 Dongmei Xin and Bicheng Yang | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 183297 15 pages doi 2011 183297 Research Article Optimality Conditions of Vector Set-Valued Optimization Problem Involving Relative Interior Zhiang Zhou1 2 1 College of Sciences Shanghai University Shanghai 200444 China 2 Department of Applied Mathematics Chongqing University of Technology Chongqing 400054 China Correspondence should be addressed to Zhiang Zhou zhLang@ Received 26 October 2010 Revised 25 December 2010 Accepted 22 January 2011 Academic Editor Sin E. Takahasi Copyright 2011 Zhiang Zhou. 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. Firstly a generalized weak convexlike set-valued map involving the relative interior is introduced in separated locally convex spaces. Secondly a separation property is established. Finally some optimality conditions including the generalized Kuhn-Tucker condition and scalarization theorem are obtained. 1. Introduction In mathematical programming set-valued optimization is a very important topic. Since the 1980s many authors have paid attention to it. Some international journals such as Set-Valued and Variational Analysis original name Set-Valued Analysis were also established. Theories and applications are widely developed. Rong and Wu 1 Li 2 and Yang 3 and Yang 4 introduced cone convexlikeness subconvexlikeness generalized subconvexlikeness and nearly subconvexlikeness respectively. In these generalized convex set-valued maps it is clear that nearly subconvexlikeness is the weakest. We find that in the above-mentioned papers the convex cone has a nonempty topological interior. However it is possible that the topological interior of the convex cone is empty. For instance if C r 0 r 0 c R2 then the topological interior of C is empty. In order to study .
