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

• Published in: AIMS mathematics Vol. 6; no. 10; pp. 11494 - 11507
• Main Authors: Hai, XuRan, Wang, ShuHong
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: convex function; erdélyi-kober fractional integrals; error estimations; hermite-hadamard inequality; riemann-liouville fractional integrals
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021666

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.