Some Generalizations of Different Types of Quantum Integral Inequalities for Differentiable Convex Functions with Applications

被引：12

作者：

Zhao, Dafang ^{[1
,2
]}

Ali, Muhammad Aamir ^{[3
]}

Luangboon, Waewta ^{[4
]}

Budak, Huseyin ^{[5
]}

Nonlaopon, Kamsing ^{[4
]}

机构：

[1] Hubei Normal Univ, Sch Math & Stat, Huangshi 435002, Hubei, Peoples R China

[2] Chinese Acad Sci, Northwest Inst Ecoenvironm & Resources, Lanzhou 730000, Peoples R China

[3] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Peoples R China

[4] Khon Kaen Univ, Fac Sci & Arts, Dept Math, Khon Kaen 40002, Thailand

[5] Duzce Univ, Fac Sci & Arts, Dept Math, TR-81620 Duzce, Turkey

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 03期

基金：

湖北省教育厅重点项目;

关键词：

midpoint inequalities; trapezoidal inequalities; Ostrowski's inequalities; Simpson's inequalities; quantum calculus; convex functions; HERMITE-HADAMARD INEQUALITIES; MIDPOINT TYPE INEQUALITIES; (ALPHA;

D O I：

10.3390/fractalfract6030129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson's type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results.

引用

页数：21

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