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.
Citation: XuRan Hai, ShuHong Wang. Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals[J]. AIMS Mathematics, 2021, 6(10): 11494-11507. 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.
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XuRan Hai, ShuHong Wang. Hermite-Hadamard type inequalities based on the Erdélyi-Kober fractional integrals[J]. AIMS Mathematics, 2021, 6(10): 11494-11507. doi: 10.3934/math.2021666
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