有关广义 (h,m)-预不变凸函数的Ostrowski型不等式及其应用

doi:10.13371/j.cnki.chin.q.j.m.2024.03.005

数学季刊 ›› 2024, Vol. 39 ›› Issue (3): 270-287.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.005

有关广义 (h,m)-预不变凸函数的Ostrowski型不等式及其应用

School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China

收稿日期:2023-03-06 出版日期:2024-09-30 发布日期:2024-09-30
通讯作者: LIAN Tie-yan (1978-), female, native of Weinan, Shaanxi, associate professor of Shaanxi University of Science & Technology, M.S.D., engages in fuzzy integral and its applications. E-mail:liantieyan@sust.edu.cn
作者简介: LI Ran (1997-), female, native of Kaifeng, Henan, graduate student of Shaanxi University of Science & Technology, engages in fuzzy integral and its applications; LIAN Tie-yan (1978-), female, native of Weinan, Shaanxi, associate professor of Shaanxi University of Science & Technology, M.S.D., engages in fuzzy integral and its applications.
基金资助:
Supported by the National Natural Science Foundation of China (Grant No. 11801342) and the Natural Science Foundation of Shaanxi Province (Grant No. 2023-JC-YB-043).

Ostrowski’s Type Inequalities for Generalized (h,m)−Preinvex Functions with Its Applications

School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China

Received:2023-03-06 Online:2024-09-30 Published:2024-09-30
Contact: LIAN Tie-yan (1978-), female, native of Weinan, Shaanxi, associate professor of Shaanxi University of Science & Technology, M.S.D., engages in fuzzy integral and its applications. E-mail:liantieyan@sust.edu.cn
About author: LI Ran (1997-), female, native of Kaifeng, Henan, graduate student of Shaanxi University of Science & Technology, engages in fuzzy integral and its applications; LIAN Tie-yan (1978-), female, native of Weinan, Shaanxi, associate professor of Shaanxi University of Science & Technology, M.S.D., engages in fuzzy integral and its applications.
Supported by:
Supported by the National Natural Science Foundation of China (Grant No. 11801342) and the Natural Science Foundation of Shaanxi Province (Grant No. 2023-JC-YB-043).

摘要/Abstract

摘要： A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.

关键词: Generalized (h,m)?preinvex function, Hermite?Hadamard inequality, Ostrowski inequality, Simpson inequality

Abstract: A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.

Key words: Generalized (h,m)?preinvex function, Hermite?Hadamard inequality, Ostrowski inequality, Simpson inequality

中图分类号:

O178

李然, 连铁艳. 有关广义 (h,m)-预不变凸函数的Ostrowski型不等式及其应用[J]. 数学季刊, 2024, 39(3): 270-287.

LI Ran, LIAN Tie-yan. Ostrowski’s Type Inequalities for Generalized (h,m)−Preinvex Functions with Its Applications[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(3): 270-287.

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有关广义 (h,m)-预不变凸函数的Ostrowski型不等式及其应用

Ostrowski’s Type Inequalities for Generalized (h,m)−Preinvex Functions with Its Applications

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