In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epideriva...In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.展开更多
SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is...SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This展开更多
完备内积空间中有界闭凸集的非扩张自映射有不动点。概率度量空间的非扩张自映射也有类似的不动点定理。完备变内积空间中,变内积引导出一个普通内积,作为内积空间和概率度量空间,上述结论显然是成立的。但变内积空间关于概率范数的非...完备内积空间中有界闭凸集的非扩张自映射有不动点。概率度量空间的非扩张自映射也有类似的不动点定理。完备变内积空间中,变内积引导出一个普通内积,作为内积空间和概率度量空间,上述结论显然是成立的。但变内积空间关于概率范数的非扩张自映射是否也有不动点呢?在本文中,我们证明了,若 B 是完备变内积空间 H 的紧凸集,T 是从 B 到 B的非扩张映射,I-T 是单调映射,则 T 有不动点,而且 T 的不动点组成的集合是凸集。展开更多
基金supported by the National Nature Science Foundation of China(11431004,11471291)the General Project of Chongqing Frontier and Applied Foundation Research(cstc2015jcyj A00050)the Key Project of Chongqing Frontier and Applied Foundation Research(cstc2017jcyj BX0055,cstc2015jcyj BX0113)
文摘In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.
文摘SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This
文摘完备内积空间中有界闭凸集的非扩张自映射有不动点。概率度量空间的非扩张自映射也有类似的不动点定理。完备变内积空间中,变内积引导出一个普通内积,作为内积空间和概率度量空间,上述结论显然是成立的。但变内积空间关于概率范数的非扩张自映射是否也有不动点呢?在本文中,我们证明了,若 B 是完备变内积空间 H 的紧凸集,T 是从 B 到 B的非扩张映射,I-T 是单调映射,则 T 有不动点,而且 T 的不动点组成的集合是凸集。
