Integral inequalities for generalized harmonically quasi-convex functions on fractal sets
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摘要: 给出了分形实线集${\mathbb{R}}^{\alpha}(0<\alpha\leqslant1)$上广义调和拟凸函数的定义,并且建立了一些关于广义调和拟凸函数的推广的Hermite-Hadamard型和Simpson型积分不等式.最后给出了文中得到的积分不等式在分形实线上关于α型特殊均值的一些应用.
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关键词:
- 广义调和拟凸函数 /
- Hermite-Hadamard型不等式 /
- Simpson型不等式 /
- 分形集 /
- 局部分数阶积分
Abstract: In this paper, the author introduces the concept of generalized harmonically quasi-convex functions on fractal sets ${\mathbb{R}}^{\alpha}(0<\alpha\leqslant1)$ of real line numbers and establishes generalized Hermite-Hadamard and Simpson type inequalities for generalized harmonically quasi-convex functions. Some applications for α-type special means of real line numbers are given. -
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