New Inequalities of Bullen-type for Twice-Differentiable Functions via Conformable Fractional Integrals

被引：0

作者：

Fatih Hezenci ^{[1
]}

Hüseyin Budak ^{[1
]}

机构：

[1] Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce

来源：

International Journal of Applied and Computational Mathematics | 2024年 / 10卷 / 6期

关键词：

26A33; 26D07; 26D10; Bullen-type inequalities; Conformable fractional integrals; Convex functions; Riemann–Liouville fractional integrals;

D O I：

10.1007/s40819-024-01804-7

中图分类号：

学科分类号：

摘要：

In this paper, an equality for the case of twice-differentiable convex functions is established by the conformable fractional integrals. In addition, sundry Bullen-type inequalities are acquired by conformable fractional integrals for the case of twice-differentiable functions. Moreover, several Bullen-type inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Finally, we derive our important results by using special cases of obtained theorems. In future studies, the ideas and strategies for our results related Bullen-type inequalities by conformable fractional integrals may open new ways for mathematicians in this area. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

引用

共 50 条

[21] A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions [J].

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MATHEMATICA SLOVACA, 2023, 73 (03) :675-686

[22] New inequalities of Opial type for conformable fractional integrals [J].

Sarikaya, Mehmet Zeki ;

Budak, Huseyin .

TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (05) :1164-1173

[23] ON NEW GRUSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS [J].

Mumcu, I ;

Set, E. .

TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2019, 9 (04) :755-763

[24] Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions [J].

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Murtaza, Ghulam ;

Ali, Muhammad Aamir ;

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Sial, Ifra Bashir ;

Agarwal, Praveen .

AXIOMS, 2022, 11 (02)

[25] New Generalizations for Convex Functions via Conformable Fractional Integrals [J].

Ekinci, Alper ;

Eroglu, Nazlican .

FILOMAT, 2019, 33 (14) :4525-4534

[26] Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications [J].

Tseng, Kuei-Lin ;

Hwang, Shiow-Ru ;

Hsu, Kai-Chen .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (04) :651-660

[27] Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications [J].

Kashuri, Artion ;

Liko, Rozana .

INTERNATIONAL JOURNAL OF OPTIMIZATION AND CONTROL-THEORIES & APPLICATIONS-IJOCTA, 2020, 10 (02) :226-236

[28] PERTURBED FRACTIONAL NEWTON-TYPE INEQUALITIES BY TWICE DIFFERENTIABLE FUNCTIONS [J].

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Kara, Hasan ;

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HONAM MATHEMATICAL JOURNAL, 2023, 45 (02) :285-299

[29] Conformable fractional Newton-type inequalities with respect to differentiable convex functions [J].

Unal, Cihan ;

Hezenci, Fatih ;

Budak, Huseyin .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2023, 2023 (01)

[30] Conformable fractional Newton-type inequalities with respect to differentiable convex functions [J].

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