It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces ...It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.展开更多
The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity o...The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.展开更多
我们开发一个理论向下，为 normed 的一个类的集合订了空格。在 normed 的 Westudy 最好的近似由元素订了空间 X 向下设定，并且为最好的近似的任何元素给必要、足够的条件由一向下关门了 X 的子集。我们也向下严格地描绘 X 的子集，并...我们开发一个理论向下，为 normed 的一个类的集合订了空格。在 normed 的 Westudy 最好的近似由元素订了空间 X 向下设定，并且为最好的近似的任何元素给必要、足够的条件由一向下关门了 X 的子集。我们也向下严格地描绘 X 的子集，并且证明那一向下 X 的子集严格地是向下如果并且仅当每它的边界点是 Chebyshev。获得的结果被用于一些 Chebyshev 对的检查(W， x ) ， x ∈ X 和 W 在此一向下关门了 X 的子集。展开更多
文摘It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.
基金the Mahani Mathematical Research Center,Iran,grant no:97/3267。
文摘The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.
文摘我们开发一个理论向下，为 normed 的一个类的集合订了空格。在 normed 的 Westudy 最好的近似由元素订了空间 X 向下设定，并且为最好的近似的任何元素给必要、足够的条件由一向下关门了 X 的子集。我们也向下严格地描绘 X 的子集，并且证明那一向下 X 的子集严格地是向下如果并且仅当每它的边界点是 Chebyshev。获得的结果被用于一些 Chebyshev 对的检查(W， x ) ， x ∈ X 和 W 在此一向下关门了 X 的子集。
