On the quadratic support of strongly convex functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 7، شماره 1، 2016، صفحه 15-20 اصل مقاله (312.48 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2015.273 | ||
| نویسندگان | ||
| S. Abbaszadeh* ؛ M Eshaghi Gordji | ||
| Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran | ||
| چکیده | ||
| In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown. | ||
| کلیدواژهها | ||
| strongly convex function؛ Hahn-Banach theorem؛ $c$-affine functions؛ quadratic support | ||
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