$(\varphi_1, \varphi_2)$-variational principle | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 22، دوره 8، شماره 2، 2017، صفحه 251-261 اصل مقاله (369.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1664.1439 | ||
| نویسندگان | ||
| Abdelhakim Maaden* ؛ Stouti Abdelkader | ||
| Universit'e Sultan Moulay Slimane, Facult'e des Sciences et Techniques, Laboratoire de Math'ematiques et Applications, B.P. 523, Beni-Mellal 23000, Marocco | ||
| چکیده | ||
| 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 [On the variational principle, J. Math. Anal. Appl. 47 (1974) 323-353], that of Borwein-Preiss [A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. 303 (1987) 517-527] and that of Deville-Godefroy-Zizler [Un principe variationel utilisant des fonctions bosses, C. R. Acad. Sci. (Paris). Ser.I 312 (1991) 281--286] and [A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions, J. Funct. Anal. 111 (1993) 197-212]. | ||
| کلیدواژهها | ||
| $(\varphi_1, \varphi_2)$-convex function؛ $(\varphi_1, \varphi_2)$-variational principle؛ Ekeland's variational principle؛ smooth variational principle | ||
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