Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

被引：103
|
作者：
Budak, Huseyin [1 ]
Erden, Samet [2 ]
Ali, Muhammad Aamir [3 ]
机构：
[1] Duzce Univ, Fac Sci & Arts, Dept Math, Duzce, Turkey
[2] Bartin Univ, Fac Sci, Dept Math, Bartin, Turkey
[3] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 01期
关键词：
convex function; quantum derivatives; quantum integral inequalities; Simpson inequality; HERMITE-HADAMARD INEQUALITIES;
D O I：
10.1002/mma.6742
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.
引用
收藏
页码：378 / 390
页数：13
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