Generalization of quantum calculus and corresponding Hermite–Hadamard inequalities

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Saira Bano Akbar, Mujahid Abbas, Hüseyin Budak
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引用次数: 0

Abstract

The aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called \((\phi \,-\,h)\) integrals and \((\phi \,-\,h)\) derivatives, respectively. Then we investigate some implicit integral inequalities for \((\phi \,-\,h)\) integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite–Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and \(\hbar \)-convex functions defined on the non-negative part of the real line.

量子微积分的广义化和相应的赫米特-哈达马德不等式
本文的目的首先是介绍量子积分和导数的广义,它们分别被称为((\phi \,-\,h))积分和((\phi \,-\,h))导数。然后我们研究了 \((\phi\,-\,h)\) 积分的一些隐式积分不等式。我们用不同类的凸函数来证明这些对称函数的不等式。在某些假设条件下,推导出了 q 积分的 Hermite-Hadamard 型不等式。本文提出的结果适用于定义在实线非负部分上的凸、m-凸和\(\hbar \)-凸函数。
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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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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