Fractals ( IF 4.7 ) Pub Date : 2022-08-30 , DOI: 10.1142/s0218348x22501602 YONGFANG QI 1 , QINGZHI WEN 1 , GUOPING LI 2 , KECHENG XIAO 1 , SHAN WANG 1
The Hermite–Hadamard (HH)-type inequality plays a very important role in the fields of basic mathematics and applied mathematics. In recent years, many scholars have expanded and improved it. Although we have achieved some research results about HH-type inequality, the research on discrete HH-type inequalities has just begun, and a lot of work needs to be improved. In this paper, we introduce -convex function and present discrete HH-type inequalities on time scale with discrete substitution method. In addition, the Hermite–Hadamard–Fejér(HHF)-type inequalities on time scale will be obtained, where the integrand is , is -convex function on and is symmetric with respect to , our results in some special cases yield the well-known classic HHF-type inequalities. Finally, through the discrete substitution method, we get discrete fractional HH-type inequality and discrete fractional HHF-type inequality for -convex function.
中文翻译:
(s,m)-凸函数的离散 Hermite–HADAMARD 型不等式
Hermite-Hadamard (HH) 型不等式在基础数学和应用数学领域有着非常重要的作用。近年来,许多学者对其进行了扩展和改进。虽然我们在 HH 型不等式方面取得了一些研究成果,但关于离散 HH 型不等式的研究才刚刚开始,还有很多工作需要改进。在本文中,我们介绍-凸函数,并使用离散替换方法在时间尺度上呈现离散的 HH 型不等式。此外,将得到时间尺度上的 Hermite-Hadamard-Fejér(HHF) 型不等式,其中被积函数为,是-凸函数和关于对称,我们在一些特殊情况下的结果产生了著名的经典 HHF 型不等式。最后,通过离散代入法,我们得到离散分数HH型不等式和离散分数HHF型不等式-凸函数。