Taiwanese Journal of Mathematics


O. Chadli and H. Mahdioui

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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

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

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 90C47: Minimax problems [See also 49K35] 90C48: Programming in abstract spaces 49J35: Minimax problems

vector saddle point C-lower semicontinuity C-quasiconvexity KKM lemma paracompacity


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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