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

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

Abstract

© 2016, Springer Science+Business Media New York. 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	American English
Pages (from-to)	65-71
Number of pages	7
Journal	Journal of Optimization Theory and Applications
DOIs	https://doi.org/10.1007/s10957-016-0922-1
State	Published - 1 Jul 2016

Access to Document

10.1007/s10957-016-0922-1

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84961197802&origin=inward

Cite this

@article{1976dab881ff4a99afb10cea48b46c26,

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

abstract = "{\textcopyright} 2016, Springer Science+Business Media New York. 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.",

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

year = "2016",

month = jul,

day = "1",

doi = "10.1007/s10957-016-0922-1",

language = "American English",

pages = "65--71",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

}

TY - JOUR

T1 - A Note on König and Close Convexity in Minimax Theorems

AU - Luque-Vásquez, Fernando

AU - Minjárez-Sosa, J. Adolfo

AU - Mitre-Báez, Max E.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - © 2016, Springer Science+Business Media New York. 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 - © 2016, Springer Science+Business Media New York. 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.

U2 - 10.1007/s10957-016-0922-1

DO - 10.1007/s10957-016-0922-1

M3 - Article

SN - 0022-3239

SP - 65

EP - 71

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

ER -

A Note on König and Close Convexity in Minimax Theorems

Abstract

Access to Document

Fingerprint

Cite this