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

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

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[42] Some generalization of integral inequalities for twice differentiable mappings involving fractional integrals [J].

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[43] On some Newton's type inequalities for differentiable convex functions via Riemann-Liouville fractional integrals [J].

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[44] Advancements in corrected Euler-Maclaurin-type inequalities via conformable fractional integrals [J].

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[47] NEW CONFORMABLE FRACTIONAL HERMITE HADAMARD TYPE INEQUALITIES FOR HARMONICALLY CONVEX FUNCTIONS [J].

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[48] Generalizations Euler-Maclaurin-type inequalities for conformable fractional integrals [J].

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[49] NEW EXTENSIONS VERSION OF HERMITE-HADAMARD TYPE INEQUALITIES BY MEANS OF CONFORMABLE FRACTIONAL INTEGRALS [J].

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[50] New extensions of Chebyshev-Polya-Szego type inequalities via conformable integrals [J].

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