强h-凸函数的若干性质
Some Properties of the Strongly h-Convex Function
DOI: 10.12677/PM.2018.81002, PDF,    科研立项经费支持
作者: 张欣隆, 郑乔诗, 阮建苗*：浙江外国语学院数学系，浙江 杭州
关键词: 强h-凸函数；h-凸函数；上积函数；Strongly h-Convex Function； h-Convex Function； Sup-Multiplicative Function
摘要: 强h-凸函数是强凸函数和h-凸函数的推广，而后者又是凸函数、s-凸函数、Godunova-Levin函数以及P-函数等的推广。本文讨论了强h-凸函数的一些基本性质，并结合上积函数，函数列收敛等概念，对强h-凸函数的性质进行更深入的讨论。
Abstract: The strongly h-convex function is a generation of the convex function and the h-convex function, and the latter is also a common generalization of the convexity, s-convexity, the Godunova-Levin function and the P-function. In this paper, we discuss some basic properties of strongly h-convex functions, and make some presentations of them involving the notations of sup-multiplicative functions, convergence of sequence, etc.
文章引用：张欣隆, 郑乔诗, 阮建苗. 强h-凸函数的若干性质[J]. 理论数学, 2018, 8(1): 8-13. https://doi.org/10.12677/PM.2018.81002

参考文献

[1] Varosanec, S. (2007) On h-Convexity. Journal of Mathematical Analysis and Applications, 326, 303-311. [Google Scholar] [CrossRef] 
[2] Hudzik, H. and Maligranda, L. (1994) Some Remarks on si-Convex Functions. Aequationes Mathematicae, 48, 100-111. [Google Scholar] [CrossRef] 
[3] Godunova, E.K. and Levin, V.I. (1985) Neravenstva Dlja Funkcii Sirokogo Klassa, Soderzascego Vypuklye, Monotonnye I Nekotorye Drugie Vidy Funkii. Vycislitel. Mat.i Mt Fiz., Mezvuzov. Sb. Nauc. Trudov. MGPI, Moscow, 138-142.
[4] Dragomir, S.S., Pecaric, J. and Persson, L.E. (1995) Some Inequalities of Hadamard Type. Soochow Journal of Mathematics, 21, 335-341.
[5] Burai, P. and Hazy, A. (2011) On Approximately h-Convex Functions. Journal of Convex Analysis, 18, 243-252.
[6] Hazy, A. (2011) Bernstein-Doetsch Type Results for h-Convex Functions. Mathematical Inequalities & Applications, 14, 499-508. [Google Scholar] [CrossRef] 
[7] Latif, M.A. (2010) On Some Inequalities for h-Convex Functions. Journal of Mathematical Analysis and Applications, 4, 1473-1482.
[8] Angulo, H., Gimenez, J., Moros, M. and Nikodem, K. (2011) On Strongly h-Convex Function. Annals of Functional Analysis, 2, 85-91. [Google Scholar] [CrossRef] 
[9] Polyak, B.T. (1966) Existence Theorems and Convergence of Minimizing Sequences in Extremum Problems with Restrictions. Doklady Mathematics, 7, 72-75.

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