Abstract and Applied Analysis

Minimax Theorems for Set-Valued Mappings under Cone-Convexities

Yen-Cherng Lin, Qamrul Hasan Ansari, and Hang-Chin Lai

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Abstract

The aim of this paper is to study the minimax theorems for set-valued mappings with or without linear structure. We define several kinds of cone-convexities for set-valued mappings, give some examples of such set-valued mappings, and study the relationships among these cone-convexities. By using our minimax theorems, we derive some existence results for saddle points of set-valued mappings. Some examples to illustrate our results are also given.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 310818, 26 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364476004

Digital Object Identifier
doi:10.1155/2012/310818

Mathematical Reviews number (MathSciNet)
MR3004908

Zentralblatt MATH identifier
1264.49017

Citation

Lin, Yen-Cherng; Ansari, Qamrul Hasan; Lai, Hang-Chin. Minimax Theorems for Set-Valued Mappings under Cone-Convexities. Abstr. Appl. Anal. 2012 (2012), Article ID 310818, 26 pages. doi:10.1155/2012/310818. https://projecteuclid.org/euclid.aaa/1364476004


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