$\left(φ_1, φ_2\right)-$Variational principle
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 $\left(φ_1, φ_2\right)-$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].
math.FA↗