有限区间上关于另一函数的右量子微积分和量子赫米特-哈达玛德不等式

Axioms Pub Date : 2024-07-10 DOI:10.3390/axioms13070466
A. Cuntavepanit, Sotiris K. Ntouyas, J. Tariboon
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摘要

本文研究有限区间上相对于另一个函数的右量子微积分。我们提出了一个函数相对于另一个函数的右量子导数和右量子积分的新定义,并研究了它们的基本性质。新定义概括了以前文献中已有的结果。我们通过获得凸函数、h-凸函数和修正的 h-凸函数的新赫米特-哈达玛不等式,提供了新定义的量子微积分的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Right Quantum Calculus on Finite Intervals with Respect to Another Function and Quantum Hermite–Hadamard Inequalities
In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The new definitions generalize the previous existing results in the literature. We provide applications of the newly defined quantum calculus by obtaining new Hermite–Hadamard-type inequalities for convex, h-convex, and modified h-convex functions.
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