A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

Daishi Kuroiwa; Nicolae Popovici; Matteo Rocca

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A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

机译：集值函数的锥凸性的锥拟凸性刻画

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摘要

A classical result by Crouzeix (1977) states that a real-valued function is convex if and only if any function obtained from it by adding a linear functional is quasiconvex. The principal aim of this paper is to present a similar characterization for certain cone-convex set-valued functions by means of cone-quasiconvex and affine set-valued functions.

机译：Crouzeix（1977）的经典结果指出，当且仅当通过添加线性函数从中获得的任何函数是拟凸的时，实值函数才是凸的。本文的主要目的是通过锥拟凸和仿射集值函数来对某些锥集值函数进行类似的表征。

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来源
《Set-Valued and Variational Analysis》 |2015年第2期|295-304|共10页
作者
Daishi Kuroiwa; Nicolae Popovici; Matteo Rocca;
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作者单位

Department of Mathematics and Computer Sciences Shimane University">(1);

Faculty of Mathematics and Computer Science Babeş-Bolyai University of Cluj-Napoca">(2);

Department of Economics University of Insubria">(3);

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正文语种 eng
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关键词
Set-valued affine function; Cone-convexity; Cone-quasiconvexity; Rådström’s cancellation law;

机译：集值仿射函数;锥凸性锥拟凸;拉德斯特罗姆的取消法;

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1. A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity [J] . Kuroiwa Daishi, Popovici Nicolae, Rocca Matteo Set-valued and variational analysis . 2015,第2期

机译：集值函数的锥凸性的锥拟凸性刻画
2. Minimax Theorems for Set-Valued Mappings under Cone-Convexities [J] . Yen-CherngLin, Qamrul HasanAnsari, Hang-ChinLai Abstract and applied analysis . 2012,第2期

机译：锥凸下集值映射的极小极大定理
3. Set-valued mapping monotonicity as characterization of D.C functions [J] . Lafhim Lahoussine, Ahmed Alaoui Elhilali, N. Gadhi Positivity . 2009,第2期

机译：集值映射单调性作为DC函数的表征
4. On Some Functional Characterizations of (Fuzzy) Set-Valued Random Elements [C] . Ana Colubi, Gil Gonzalez-Rodriguez International Conference on Soft Methods in Probability and Statistics . 2017

机译：关于（模糊）设定值随机元素的一些功能特征
5. Inverse limits of set-valued functions. [D] . Cornelius, Alexander Nelson. 2009

机译：集值函数的反极限。
6. SUBINTEGRALS OF SET-VALUED FUNCTIONS WITH SEMIANALYTIC GRAPHS [O] . Hubert Halkin, Edward C. Hendricks 1968

机译：具有半解析图的集值函数的子积分
7. Relationship among Various Types of Cone-Convexity of Vector-Valued Functions [O] . 田中環 1991

机译：向量值函数的各种类型的锥凸之间的关系
8. Unification and Set-Valued Functions for Functional and Logic Programming [R] . Silbermann, F. S., Jayaraman, B. 1987

机译：功能和逻辑编程的统一和集值函数

A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

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