细化修正 ( h , m ) -凸函数的卡普托分式衍生不等式

Q4 Mathematics
Muhammad Ajmal, Muhammad Rafaqat, Labeeb Ahmad
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引用次数: 0

摘要

本文介绍了一种新型的凸函数,即精炼修正的(h,m)-凸函数,它是对传统(h,m)-凸函数的概括。我们利用卡普托 k 分数导数为这一新定义建立了哈达玛式不等式。具体地说,我们推导出涉及给定函数 n 阶导数的两个积分等式,并利用它们证明了哈达玛式不等式对改进的(h,m)凸函数的卡普托 k 分导数的估计。这项研究获得的结果证明了精炼修正 (h,m) 凸函数的多功能性,以及卡普托 k 分导数在建立重要不等式方面的实用性。我们的研究为凸函数的现有知识体系做出了贡献,并为分数微积分在数学分析中的应用提供了启示。这些研究成果有可能为凸函数和分数微积分领域以及其他数学研究领域的未来研究铺平道路。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions
This paper introduces a novel type of convex function known as the refined modified (h,m)-convex function, which is a generalization of the traditional (h,m)-convex function. We establish Hadamard-type inequalities for this new definition by utilizing the Caputo k-fractional derivative. Specifically, we derive two integral identities that involve the nth order derivatives of given functions and use them to prove the estimation of Hadamard-type inequalities for the Caputo k-fractional derivatives of refined modified (h,m)-convex functions. The results obtained in this research demonstrate the versatility of the refined modified (h,m)-convex function and the usefulness of Caputo k-fractional derivatives in establishing important inequalities. Our work contributes to the existing body of knowledge on convex functions and offers insights into the applications of fractional calculus in mathematical analysis. The research findings have the potential to pave the way for future studies in the area of convex functions and fractional calculus, as well as in other areas of mathematical research.
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来源期刊
Utilitas Mathematica
Utilitas Mathematica 数学-统计学与概率论
CiteScore
0.50
自引率
0.00%
发文量
0
审稿时长
6 months
期刊介绍: Utilitas Mathematica publishes papers in all areas of statistical designs and combinatorial mathematics, including graph theory, design theory, extremal combinatorics, enumeration, algebraic combinatorics, combinatorial optimization, Ramsey theory, automorphism groups, coding theory, finite geometries, chemical graph theory, etc., as well as the closely related area of number-theoretic polynomials for enumeration.
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