分形集上广义调和拟凸函数的一些积分不等式

doi:10.3969/j.issn.1000-5641.2019.04.007

华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (4): 62-71.doi: 10.3969/j.issn.1000-5641.2019.04.007

分形集上广义调和拟凸函数的一些积分不等式

孙文兵

邵阳学院理学院, 湖南邵阳 422000

收稿日期:2018-06-01 出版日期:2019-07-25 发布日期:2019-07-18
作者简介:孙文兵,男,副教授,研究方向为解析不等式、智能算法.E-mail:swb0520@163.com.
基金资助:
国家自然科学基金（61672356）；湖南省教育厅青年项目（18B433）；邵阳市科技计划项目（2017GX09）

Integral inequalities for generalized harmonically quasi-convex functions on fractal sets

SUN Wen-bing

School of Science;Shaoyang University;Shaoyang Hunan 422000, China

Received:2018-06-01 Online:2019-07-25 Published:2019-07-18

摘要/Abstract

摘要： 给出了分形实线集R^α（0<α≤1）上广义调和拟凸函数的定义，并且建立了一些关于广义调和拟凸函数的推广的Hermite-Hadamard型和Simpson型积分不等式.最后给出了文中得到的积分不等式在分形实线上关于α型特殊均值的一些应用.

关键词: 广义调和拟凸函数, Hermite-Hadamard型不等式, Simpson型不等式, 分形集, 局部分数阶积分

Abstract: In this paper, the author introduces the concept of generalized harmonically quasi-convex functions on fractal sets R^α(0 < α ≤ 1) of real line numbers and establishes generalized Hermite-Hadamard and Simpson type inequalities for generalized harmonically quasi-convex functions. Some applications for α-type special means of real line numbers are given.

Key words: generalized harmonically quasi-convex function, Hermite-Hadamard type inequalities, Simpson type inequalities, fractal sets, local fractional integral

中图分类号:

O178

孙文兵. 分形集上广义调和拟凸函数的一些积分不等式[J]. 华东师范大学学报(自然科学版), 2019, 2019(4): 62-71.

SUN Wen-bing. Integral inequalities for generalized harmonically quasi-convex functions on fractal sets[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(4): 62-71.

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分形集上广义调和拟凸函数的一些积分不等式

Integral inequalities for generalized harmonically quasi-convex functions on fractal sets

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[1]	孙文兵. 分形空间上的新Hadamard型不等式及应用[J]. 华东师范大学学报(自然科学版), 2017, 2017(6): 33-41.
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