有关(α,m)-对数凸函数的Hermite-Hadamard型积分不等式
Integral Inequalities of Hermite-Hadamard Style for (α, m)-Logarithmically Convex Functions
DOI: 10.12677/PM.2021.111014, PDF, HTML, 下载: 520  浏览: 752  科研立项经费支持
作者: 黄 滢, 韩盼盼, 齐 静, 王 芳, 王 文*, 魏茂森：合肥师范学院数学与统计学院, 安徽 合肥
关键词: Hermite-Hadamard型不等式；(α；m)-对数凸函数；不等式；Hermite-Hadamard’s Inequality； (α；m)-Logarithmically Convex Function； Inequality
摘要: 本文主要建立一些新的涉及(α, m)对数凸函数的Hermite-Hadamard型积分不等式。
Abstract: The aim of this paper is to establish several new Hermite-Hadamard style inequalities for (α, m)-logarithmically convex function.
文章引用：黄滢, 韩盼盼, 齐静, 王芳, 王文, 魏茂森. 有关(α,m)-对数凸函数的Hermite-Hadamard型积分不等式[J]. 理论数学, 2021, 11(1): 94-102. https://doi.org/10.12677/PM.2021.111014

参考文献

[1] Mitrinovi´c, D.S., Peˇcari´c, J.E. and Fink, A.M. (1993) Classical and New Inequalities in Anal- ysis. Kluwer Academic Publishers, Dordrecht.
https://doi.org/10.1007/978-94-017-1043-5
[2] Peˇcari´c, J.E., Proschan, F. and Tong, Y.L. (1991) Convex Functions, Partial Orderings and Statistical Applications. Academic Press, Cambridge, MA.
[3] Dragomir, S.S. and Toader, G. (1993) Some Inequalities for m-Convex Functions. Studia Uni- versitatis Babes-Bolyai Mathematica, 38, 21-28.
[4] Bai, R.F., Qi, F. and Xi, B.Y. (2013) Hermite-Hadamard Type Inequalities for the m- and (α;m)-Logarithmically Convex Functions. Filomat, 27, 1-7.
http://www.pmf.ni.ac.rs/filomat
https://doi.org/10.2298/FIL1301001B
[5] Bakula, M.K., O¨ zdemir, M.E. and Peˇcri´c, J. (2008) Hadamard Type Inequalities for m-Convex and (α;m)-Convex Functions. Journal of Inequalities in Pure and Applied Mathematics, 9, Article No. 96.
[6] Xi, B.Y., Bai, R.F. and Qi, F. (2012) Hermite-Hadamard Type Inequalities for the m- and (α;m)-Geometrically Convex Functions. Aequationes Mathematicae, 84, 261-269.
https://doi.org/10.1007/s00010-011-0114-x
[7] Kirmac, U.S. and O¨ zdemir, M.E. (2004) Some Inequalities for Mappings Whose Derivatives Are Bounded and Applications to Specials Means of Real Numbers. Applied Mathematics Letters, 17, 641-645.
https://doi.org/10.1016/S0893-9659(04)90098-5
[8] Dragomir, S.S. (1992) Two Functions in Connection to Hadamard’s Inequalities. Journal of Mathematical Analysis and Applications, 167, 49-56.
https://doi.org/10.1016/0022-247X(92)90233-4
[9] Zhang, T.Y., Ji, A.P. and Qi, F. (2012) On Integral Inequalities of Hermite-Hadamard Type for s-Geometrically Convex Functions. Abstract and Applied Analysis, 2012, Article ID: 560586.
https://doi.org/10.1155/2012/560586
[10] Wang, W. and Qi, J.B. (2017) Some New Estimates of Hermite-Hadmard Inequalities for Harmonically Convex Functions with Applications. International Journal of Analysis and Ap- plications, 13, 15-21.

为你推荐