## Taiwanese Journal of Mathematics

### EXISTENCE RESULTS FOR VECTOR SADDLE POINTS PROBLEMS

#### Abstract

In this paper, we study the existence of solutions for vector saddle points problems in a general setting. Our approach, first, is based on the KKM lemma and a relaxation of the $C-$ lower semicontinuity notion introduced by T.Tanaka by means of an extension to the vector setting of a Brézis-Nirenberg-Stampacchia condition, and arguments from generalized convexity. This leads us to generalize and improve some new existence results on vector saddle points problems. In the second approach, we establish an existence result for vector saddle point problems under a paracompacity assumption.

#### Article information

Source
Taiwanese J. Math., Volume 16, Number 2 (2012), 429-444.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406594

Digital Object Identifier
doi:10.11650/twjm/1500406594

Mathematical Reviews number (MathSciNet)
MR2892891

Zentralblatt MATH identifier
1268.90124

#### Citation

Chadli, O.; Mahdioui, H. EXISTENCE RESULTS FOR VECTOR SADDLE POINTS PROBLEMS. Taiwanese J. Math. 16 (2012), no. 2, 429--444. doi:10.11650/twjm/1500406594. https://projecteuclid.org/euclid.twjm/1500406594

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