Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

被引：19

作者：

Fahad, Asfand ^{[1
,2
]}

Butt, Saad Ihsaan ^{[3
]}

Bayraktar, Bahtiyar ^{[4
]}

Anwar, Mehran ^{[3
]}

Wang, Yuanheng ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Peoples R China

[2] Bahauddin Zakariya Univ Multan, Ctr Adv Studies Pure & Appl Math, Multan 60800, Pakistan

[3] COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, Pakistan

[4] Uludag Univ, Dept Math & Sci Educ, TR-16059 Bursa, Turkiye

来源：

AXIOMS | 2023年 / 12卷 / 07期

基金：

中国国家自然科学基金;

关键词：

convex functions; Bullen's inequality; Hadamard inequality; Holder inequality; power mean; fractional integral operators; HADAMARD; HERMITE;

D O I：

10.3390/axioms12070691

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms of fractional integral operators. Based on this new identity, some generalized Bullen-type inequalities are obtained by employing convexity properties. Concrete examples are given to illustrate the results, and the correctness is confirmed by graphical analysis. An analysis is provided on the estimations of bounds. According to calculations, improved Holder and power mean inequalities give better upper-bound results than classical inequalities. Lastly, some applications to quadrature rules, modified Bessel functions and digamma functions are provided as well.

引用

页数：26

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[3]

Bayraktar B, 2020, TWMS J APPL ENG MATH, V10, P288

[4]

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