On M-convex functions

被引：4

作者：

Awan, Muhammad Uzair ^{[1
]}

Noor, Muhammad Aslam ^{[2
]}

Du, Tingsong ^{[3
]}

Noor, Khalida Inayat ^{[2
]}

机构：

[1] GC Univ, Dept Math, Faisalabad, Pakistan

[2] COMSATS Univ Islamabad, Dept Math, Islamabad, Pakistan

[3] China Three Gorges Univ, Coll Sci, Dept Math, Yichang, Peoples R China

来源：

AIMS MATHEMATICS | 2020年 / 5卷 / 03期

关键词：

convex; M-convex; log-M-convex; quasi M-convex; Hermite-Hadamard inequality; fractional; quantum; HERMITE-HADAMARD INEQUALITIES; INTEGRAL-INEQUALITIES; DIFFERENTIABLE MAPPINGS; BOUNDS;

D O I：

10.3934/math.2020157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we introduce the notion of M-convex functions, log-M-convex functions and the notion of quasi M-convex functions. We derive some new analogues of Hermite-Hadamard like inequalities associated with M-convex functions by using the concepts of ordinary, fractional and quantum calculus. The main results of this paper may be useful where bounds for natural phenomena described by integrals such as mechanical work are frequently required. These results are also helpful in the field of numerical analysis where error analysis is required.

引用

页码：2376 / 2387

页数：12

共 26 条

[1] q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions [J].