Modified class of hyperbolic p-convex function with application to integral inequalities

IF 6 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Ain Shams Engineering Journal Pub Date : 2025-05-13 DOI:10.1016/j.asej.2025.103445

Xiaoming Wang , Khuram Ali Khan , Saima Riaz , Ammara Nosheen , Y.S. Hamed

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引用次数: 0

Abstract

In this paper, the new class of modified hyperbolic p-convex functions is introduced and some of their basic algebraic properties are presented. The motivation behind for introducing this new class is that it can solve more complicated problems, such as those with hyperbolic structures and fractional calculus, which are often inadequately handled by classical convex functions. By utilizing this modified class, some new integral inequalities related to the Hermite-Hadamard (H-H) inequality are derived. A particular identity for differentiable functions is also used that enables an extension and improvement of the classical H-H inequality. This work explores the relationships between these modified hyperbolic p- convex functions and other classes of convex functions, demonstrating the superiority of the newly obtained inequalities over previous findings. Finally, several examples with graphs are provided to illustrate the validity of the newly established inequalities, and a comparison with earlier results highlights their enhanced applicability and significance.

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修正的双曲p-凸函数类及其在积分不等式中的应用

本文介绍了一类新的修正双曲p-凸函数，并给出了它们的一些基本代数性质。引入这个新类背后的动机是，它可以解决更复杂的问题，例如那些具有双曲结构和分数微积分的问题，这些问题通常无法由经典凸函数充分处理。利用这个改进的类，导出了与Hermite-Hadamard （H-H）不等式有关的一些新的积分不等式。本文还使用了可微函数的一个特殊恒等式，对经典H-H不等式进行了推广和改进。本文探讨了这些修正的双曲p-凸函数与其他类型的凸函数之间的关系，证明了新得到的不等式相对于以前的发现的优越性。最后，给出了几个图的例子来说明新建立的不等式的有效性，并与以前的结果进行了比较，突出了它们增强的适用性和意义。

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

Ain Shams Engineering Journal Engineering-General Engineering

CiteScore

10.80

自引率

13.30%

发文量

441

审稿时长

49 weeks

期刊介绍： in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance. Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.