Meng, Zhiqing Hahn-Banach theorem of set-valued map. (English) Zbl 0941.46004 Appl. Math. Mech., Engl. Ed. 19, No. 1, 59-66 (1998). Summary: We prove a generalized Hahn-Banach theorem by using the concept of efficiency for \(K\)-convex multifunctions and \(K\)-sublinear multifunctions in partially ordered locally convex topological vector space. Cited in 5 Documents MSC: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators 46A40 Ordered topological linear spaces, vector lattices 47H04 Set-valued operators Keywords:generalized Hahn-Banach theorem; \(K\)-convex multifunction; \(K\)-sublinear multifunction; partially ordered locally convex topological vector space PDFBibTeX XMLCite \textit{Z. Meng}, Appl. Math. Mech., Engl. Ed. 19, No. 1, 59--66 (1998; Zbl 0941.46004) Full Text: DOI References: [1] L. V. Kantorovich and G. P. Akilov, Functional analysis. Liu Zheng, i. e. translating, Beijing, Higher Education Publishers, (1982), 113–115. (Chinese version) · Zbl 0484.46003 [2] Ruan Guozhen, Dual Hahn-Banach Theorem,The Jouanal of Xiangtan University 14, 2 (1992), 52–57. [3] F. H. Clarke,Opitimization and Nonsmooth Analysis, New York: A Wiley Interscience Publication (1983), 24–109. [4] Y. Sawaragi, et al.,Theory of Multiobjective Optimization, Academic Press, Inc. Orlando (1985). · Zbl 0566.90053 [5] Hu Yuda, Efficiency theory of multiobjective programming, Shanghai, Shanghai Scientific and Technical Publishers, (1994). · Zbl 0809.90113 [6] Chen Guangya and Wang Yuyun, Generalized Hahn-Banach theorems and subdifferential of set-valued,The System Science and Mathematics,5, 3 (1985), 223–230. · Zbl 0593.46008 [7] Meng Zhiqing, et al., The optimality conditions for weak efficient solution of vectoroi optimization of set-valued function,The Jouanal of Xiangtan University,17, 4 (1995), 24–27. · Zbl 0844.90077 [8] J. P. Aubin and I. Ekeland,Applied Nonlinear Analysis, John Wiley and Sons, New York (1984). · Zbl 0641.47066 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.