(\varphi_۱, \varphi_۲)-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(\varphi_۱, \varphi_۲\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 [On the variational principle,  J. Math. Anal. Appl. ۴۷ (۱۹۷۴)  ۳۲۳-۳۵۳], that of Borwein-Preiss [A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. ۳۰۳ (۱۹۸۷) ۵۱۷-۵۲۷] and that of Deville-Godefroy-Zizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser.I  ۳۱۲ (۱۹۹۱) ۲۸۱--۲۸۶] and [A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal. ۱۱۱ (۱۹۹۳) ۱۹۷-۲۱۲].

کلیدواژه ها:

(varphi_۱ ، varphi_۲)-convex function ، (varphi_۱ ، varphi_۲)-variational principle ، Ekeland's variational principle ، smooth variational principle