Fractional Newton-type integral inequalities by means of various function classes

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-08-04 DOI:10.1002/mma.10378

Fatih Hezenci, Hüseyin Budak

引用次数: 0

Abstract

The authors of the paper present a method to examine some Newton-type inequalities for various function classes using Riemann-Liouville fractional integrals. Namely, some fractional Newton-type inequalities are established by using convex functions. In addition, several fractional Newton-type inequalities are proved by using bounded functions by fractional integrals. Moreover, we construct some fractional Newton-type inequalities for Lipschitzian functions. Furthermore, several Newton-type inequalities are acquired by fractional integrals of bounded variation. Finally, we provide our results by using special cases of obtained theorems and examples.

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利用各种函数类的分数牛顿型积分不等式

本文作者提出了一种方法，利用黎曼-刘维尔分数积分来研究各种函数类的一些牛顿型不等式。也就是说，利用凸函数建立了一些分数牛顿型不等式。此外，通过分数积分使用有界函数证明了几个分数牛顿型不等式。此外，我们还为 Lipschitzian 函数构建了一些分数牛顿型不等式。此外，我们还通过有界变分积分获得了几个牛顿型不等式。最后，我们利用所获定理的特例和示例给出了我们的结果。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.

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