Taiwanese Journal of Mathematics

MINIMAX THEOREMS FOR VECTOR-VALUED MAPPINGS IN ABSTRACT CONVEX SPACES

Ming-Ge Yang, Jiu-Ping Xu, Nan-Jing Huang, and Su-Jane Yu

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Abstract

In this paper, we introduce the concepts of $C$-quasiconcave mappings and properly $C$-quasiconcave mappings in abstract convex spaces. By using the Fan-Browder type fixed point theorem and the maximal element theorem, we establish some minimax theorems for vector-valued mappings in abstract convex spaces. We also give some examples to illustrate our results.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 719-732.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405816

Digital Object Identifier
doi:10.11650/twjm/1500405816

Mathematical Reviews number (MathSciNet)
MR2655796

Zentralblatt MATH identifier
1197.49004

Subjects
Primary: 49J35: Minimax problems 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]

Keywords
abstract convex space $C$-quasiconcave properly $C$-quasiconcave fixed point maximal element

Citation

Yang, Ming-Ge; Xu, Jiu-Ping; Huang, Nan-Jing; Yu, Su-Jane. MINIMAX THEOREMS FOR VECTOR-VALUED MAPPINGS IN ABSTRACT CONVEX SPACES. Taiwanese J. Math. 14 (2010), no. 2, 719--732. doi:10.11650/twjm/1500405816. https://projecteuclid.org/euclid.twjm/1500405816


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