A Note on König and Close Convexity in Minimax Theorems

Fernando Luque-Vásquez; J. Adolfo Minjárez-Sosa; Max E. Mitre-Báez

doi:10.1007/s10957-016-0922-1

A Note on König and Close Convexity in Minimax Theorems

Fernando Luque-Vásquez, J. Adolfo Minjárez-Sosa^*, Max E. Mitre-Báez

^*Corresponding author for this work

Departamento de Matemáticas

Research output: Contribution to journal › Article › peer-review

Abstract

We give an example of a real-valued function defined on the Cartesian product of two compact sets, which is König convex but not closely convex. Additionally, we prove that under suitable conditions, König convexity implies close convexity.

Original language	English
Pages (from-to)	65-71
Number of pages	7
Journal	Journal of Optimization Theory and Applications
Volume	170
Issue number	1
DOIs	https://doi.org/10.1007/s10957-016-0922-1
State	Published - 1 Jul 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Close convexity
König convexity
Minimax theorems

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10.1007/s10957-016-0922-1

Cite this

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title = "A Note on K{\"o}nig and Close Convexity in Minimax Theorems",

abstract = "We give an example of a real-valued function defined on the Cartesian product of two compact sets, which is K{\"o}nig convex but not closely convex. Additionally, we prove that under suitable conditions, K{\"o}nig convexity implies close convexity.",

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author = "Fernando Luque-V{\'a}squez and Minj{\'a}rez-Sosa, {J. Adolfo} and Mitre-B{\'a}ez, {Max E.}",

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AU - Luque-Vásquez, Fernando

AU - Minjárez-Sosa, J. Adolfo

AU - Mitre-Báez, Max E.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We give an example of a real-valued function defined on the Cartesian product of two compact sets, which is König convex but not closely convex. Additionally, we prove that under suitable conditions, König convexity implies close convexity.

AB - We give an example of a real-valued function defined on the Cartesian product of two compact sets, which is König convex but not closely convex. Additionally, we prove that under suitable conditions, König convexity implies close convexity.

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KW - König convexity

KW - Minimax theorems

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DO - 10.1007/s10957-016-0922-1

M3 - Artículo

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JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

ER -

A Note on König and Close Convexity in Minimax Theorems

Abstract

Bibliographical note

Keywords

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