保形分式积分中牛顿型不等式的误差边界研究

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-05-28 DOI:10.1515/ms-2024-0024

Hüseyin Budak, Cihan Ünal, Fatih Hezenci

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引用次数: 0

摘要

本文作者提出了一种新颖的方法，利用保角分数算子来检验积分等式。通过利用这个等式，对新建立的等式取模，证明了可微凸函数的一些牛顿式不等式。此外，我们还利用荷尔德不等式和幂均不等式证明了一些牛顿型不等式。此外，我们还利用已获得不等式的特殊选择提出了一些新结果。最后，我们给出了一些有界变分函数的保角牛顿式不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A study on error bounds for Newton-type inequalities in conformable fractional integrals

The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the Hölder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation.

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.