局部分数阶积分下关于广义调和<em>s</em>-凸函数的Ostrowski型不等式

doi:10.3785/j.issn.1008-9497.2018.05.007

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摘要基于分形集中局部分数阶微积分理论，建立了一个涉及局部分数阶积分的恒等式.利用此恒等式，得到了一些关于广义调和s-凸函数的推广的Ostrowski型不等式.

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	孙文兵

关键词 ： Ostrowski型不等式, 广义调和s-凸函数, 分形集, 局部分数阶积分

Abstract：Based on the theory of local fractional calculus on fractal sets, the author established an identity involving local fractional integrals. Using the identity, some generalized Ostrowski type inequalities for generalized harmonically s-convex functions were obtained.

Key words： Ostrowski type inequality generalized harmonically s-convex function fractal set local fractional integral

收稿日期: 2018-01-11

ZTFLH:

O178

基金资助:Supported by the National Natural Science Foundations of China(61672356); Shaoyang City Science and Technology Plan Project (2017GX09).

作者简介: 孙文兵(1978-),ORCID:http://orcid.org/0000-0002-5673-4519,male,master,associate professor,the field of interest is analytic inequality.

引用本文:

孙文兵. 局部分数阶积分下关于广义调和s-凸函数的Ostrowski型不等式[J]. 浙江大学学报（理学版）, 2018, 45(5): 555-561.
SUN Wenbing. Ostrowski type inequalities for generalized harmonically s-convex functions via local fractional integrals. Journal of ZheJIang University(Science Edition), 2018, 45(5): 555-561.

链接本文:

http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.05.007 或 http://www.zjujournals.com/sci/CN/Y2018/V45/I5/555

[1] OSTROWKI A. Über die absolute abweichung einer differentiebaren funktion von ihren integralmittelwert[J].Comment Math Helv,1938(10):226-227.
[2] LIU Z. A note on Ostrowski type inequalities related to some s-convex functions in the second sense[J].Bull Korean Math Soc, 2012,49(4):775-785.
[3] ISCAN I. Ostrowski type inequalities for harmonically s-convex functions[J].Math C A, 2013(7):1-11.
[4] ALOMARI M, DARUS M, DRAGOMIR S S, et al. Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense[J].Applied Mathematics Letters, 2010,23:1071-1076.
[5] ISCAN I. Hermite-Hadamard type inequalities for harmonically convex functions[J].Hacet J Math Stat, 2014,43(6):935-942.
[6] YANG X J. Advanced Local Fractional Calculus and Its Applications[M]. NewYork:World Science Publisher, 2012.
[7] YANG X J.Local Fractional Functional Analysis and Its Applications[M]. Hong Kong:Asian Academic Publisher, 2011.
[8] YANG X J, GAO F, SRIVASTAVA H M. New rheological models within local fractional derivative[J]. Rom Rep Phys, 2017,69(3):113.
[9] MO H, SUI X, YU D. Generalized convex functions on fractal sets and two related inequalities[J].Abstract and Applied Analysis, 2014, Article ID 636751.
[10] MO H, SUI X. Generalized s-convex functions on fractal sets[J]. Abstr Appl Anal, 2014, Article ID 254731
[11] ERDENA S, SARIKAYA M Z. Generalized Pompeiu type inequalities for local fractional integrals and its applications[J].Applied Mathematics and Computation, 2016,274:282-291.
[12] SUN W B, LIU Q. New inequalities of Hermite-Hadamard type for generalized convex functions on fractal sets and its applications[J].Journal of Zhejiang University(Science Edition), 2017,44(1):47-52.
[13] SUN W B. On the generalization of two classes of integral inequalities on fractal sets[C].Symposiumon Advanced Computational Methods for Linear and Nonlinear Heat and Fluid Flow 2017& Advanced Computational Methods in Applied Science 2017& Fractional (Fractal) Calculus and Applied Analysis. Xuzhou:China University of Mining and technology, 2017.
[14] CHEN G, SRIVASTAVA H M, WANG P, et al. Some further generalizations of Hölder's inequality and related results on fractal space[J].Abstract and Applied Analysis, 2014, Article ID 832802. http://dx.doi.org/10.1155/2014/832802.