The purpose of this work is to investigate some inequalities for generalized s-convexity on fractal sets ℝα, which are associated with Simpson-like inequalities. To this end, an improved version of Hölder inequality and a Simpson-like identity on fractal sets are established, in view of which we give several estimation-type results involving Simpson-like inequalities for the first-order differentiable mappings. Moreover, we provide five examples to illustrate our results. As applications with respect to local fractional integrals, we derive two inequalities according to α-type special means and generalized probability density functions.

中文翻译：

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分形集上 HÖLDER 积分不等式的改进和一些相关的辛普森不等式

这项工作的目的是调查一些不等式s-分形集上的凸性ℝα，这与辛普森式的不等式有关。为此，建立了一个改进的Hölder不等式和分形集上的类辛普森恒等式，鉴于此，我们给出了几个涉及一阶可微映射的类辛普森不等式的估计类型结果。此外，我们提供了五个例子来说明我们的结果。作为局部分数积分的应用，我们根据下式推导出两个不等式α-型特殊手段和广义概率密度函数。