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arXiv · 1610.05915

$\left(\varphi_1, \varphi_2\right)-$Variational principle

Abdelhakim Maaden·Abdelkader Stouti
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Abstract

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $\left(\varphi_1, \varphi_2\right)-$convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [18], that of Borwein-Preiss [6] and that of Deville-Godefroy-Zizler [14, 15].

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Abdelhakim Maaden, Abdelkader Stouti. 2016-10-19. $\left(\varphi_1, \varphi_2\right)-$Variational principle. https://arxiv.org/abs/1610.05915

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