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

[31] CHEBYSHEV TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS [J].

Set, Erhan ;

Akdemir, Ahmet Ocak ;

Mumcu, Ilker .

MISKOLC MATHEMATICAL NOTES, 2019, 20 (02) :1227-1236

[32] Hermite-Hadamard-Mercer Inequalities Associated with Twice-Differentiable Functions with Applications [J].

Ali, Muhammad Aamir ;

Sitthiwirattham, Thanin ;

Kobis, Elisabeth ;

Hanif, Asma .

AXIOMS, 2024, 13 (02)

[33] Hermite-Hadamard Type Inequalities for Twice Differantiable Functions via Generalized Fractional Integrals [J].

Budak, Huseyin ;

Ertugral, Fatma ;

Pehlivan, Ebru .

FILOMAT, 2019, 33 (15) :4967-4979

[34] Jensen type inequalities for twice differentiable functions [J].

El Frissi, Abdallah ;

Belaidi, Benharrat ;

Lareuch, Zinelaabidine .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2012, 5 (05) :350-356

[35] Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for p-convex functions via conformable fractional integrals [J].

Naila Mehreen ;

Matloob Anwar .

Journal of Inequalities and Applications, 2020

[36] On Some Integral Inequalities via Conformable Fractional Integrals [J].

Akdemir, Ahmet Ocak ;

Deniz, Erhan ;

Yuksel, Ebru .

APPLIED MATHEMATICS AND NONLINEAR SCIENCES, 2021, 6 (01) :489-498

[37] New parameterized inequalities for twice differentiable functions [J].

Budak, Huseyin ;

Kara, Hasan ;

Hezenci, Fatih ;

Sarikaya, Mehmet Zeki .

FILOMAT, 2023, 37 (12) :3737-3753

[38] Opial-type inequalities for conformable fractional integrals [J].

Sarikaya, Mehmet Zeki ;

Budak, Huseyin .

JOURNAL OF APPLIED ANALYSIS, 2019, 25 (02) :155-163

[39] CONFORMABLE FRACTIONAL INTEGRALS AND RELATED NEW INTEGRAL INEQUALITIES [J].

Akdemir, Ahmet Ocak ;

Ekinci, Alper ;

Set, Erhan .

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2017, 18 (04) :661-674

[40] HERMITE-HADAMARD TYPE INEQUALITIES FOR CONFORMABLE INTEGRALS VIA η-CONVEX FUNCTIONS [J].

Khurshid, Yousaf ;

Khan, Muhammad Adil .

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2023, 38 (01) :77-90

← 1 2 3 4 5 →