Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals

AIMS Mathematics

ShuHong Wang¹  XuRan Hai¹ 

[1] College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao 028000, China;

关键词: hermite-hadamard inequality;    convex function;    erdélyi-kober fractional integrals;    riemann-liouville fractional integrals;    error estimations;   

DOI  :  10.3934/math.2021666

来源: DOAJ

【 摘 要 】

In the paper, based on Erdélyi-Kober fractional integrals $ ^\rho \mathcal{K}^\alpha_{\chi+}f $ and $ ^\rho \mathcal{K}^\alpha_{\chi-}f $ for any $ \chi\in[a, b] $ with $ f\in\mathfrak{X}_c^p(a, b) $, authors establish some new Hermite-Hadamard type inequalities for convex function. The obtained inequalities generalize the corresponding results for Riemann-Liouville fractional integrals by taking limits when a parameter $ \rho\rightarrow1 $. As applications, the error estimations of Hermite-Hadamard type inequality are also provided.

【 授权许可】

Unknown