Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals - Hai, XuRan; Wang, ShuHong (AIMS mathematics, 2021)
In the paper, based on Erdélyi-Kober fractional integrals $ ^ρ \mathcal{K}^α_{χ+}f $ and $ ^ρ \mathcal{K}^α_{χ-}f $ for any $ χ\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 $ ρ→1 $. As applications, the error estimations of Hermite-Hadamard type inequality are also provided.