Talha Muhammad Sadaqat, Abbas Tasawar, Li Zhixiong, Rebey Amor, Ahmed Affaq, Anjum Sanaa
Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan.
Department of Mathematics, University of Wah, Wah Cantt, 47040, Pakistan.
Heliyon. 2024 May 14;10(10):e31041. doi: 10.1016/j.heliyon.2024.e31041. eCollection 2024 May 30.
The main motivation in this article is to prove new integral identities and related results. In this paper, we deal with -convex function, Hermite-Hadamard type inequalities, and Katugampola fractional integrals. Firstly, we established the Hermite-Hadamard type inequalities for -convex function via Katugampola fractional integrals operators. After that we obtain several new identities and give new results of Holder's inequality, Jensen's integral inequality, Young's inequality, and Power mean inequality for -convex function by using Katugampola fractional integral operators. We make connections of our results with various results recognized in the literature.
本文的主要动机是证明新的积分恒等式及相关结果。在本文中，我们研究了(\alpha -)凸函数、Hermite - Hadamard型不等式以及Katugampola分数阶积分。首先，我们通过Katugampola分数阶积分算子建立了(\alpha -)凸函数的Hermite - Hadamard型不等式。之后，我们得到了几个新的恒等式，并利用Katugampola分数阶积分算子给出了(\alpha -)凸函数的Holder不等式、Jensen积分不等式、Young不等式和幂平均不等式的新结果。我们将我们的结果与文献中认可的各种结果建立了联系。
