The main objective of this paper is to establish some new Hermite–Hadamard type inequalities involving k-Riemann–Liouville fractional integrals. Using the convexity of differentiable functions some related inequalities have been proved, which have deep connection with some known results. At the end, some applications of the obtained results in error estimations of quadrature formulas are also considered.

中文翻译：

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关于涉及k分形算子的某些Hermite-Hadamard不等式

本文的主要目的是建立一些新的涉及k-Riemann-Liouville分数积分的Hermite-Hadamard型不等式。利用微分函数的凸性，已经证明了一些相关的不等式，这些不等式与一些已知的结果有很深的联系。最后，还考虑了所得结果在正交公式误差估计中的一些应用。