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

^*Autor correspondiente de este trabajo

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	65-71
Número de páginas	7
Publicación	Journal of Optimization Theory and Applications
Volumen	170
N.º	1
DOI	https://doi.org/10.1007/s10957-016-0922-1
Estado	Publicada - 1 jul. 2016

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

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10.1007/s10957-016-0922-1

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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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AU - Mitre-Báez, Max E.

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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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JO - Journal of Optimization Theory and Applications

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A Note on König and Close Convexity in Minimax Theorems

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