This work is motivated by the work of Josip Pečarić in 2013 and 1982 and the work of Srivastava in 2017. By the utilization of the diamond-$\alpha$ dynamic inequalities, which are defined as a linear mixture of the delta and nabla integrals, we present and prove very important generalized results of diamond-$\alpha$ Steffensen-type inequalities on a general time scale. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

中文翻译：

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一般时间尺度上的各种动态 Steffensen 型不等式

这项工作的动机是 Josip Pečarić 在 2013 年和 1982 年的工作以及 Srivastava 在 2017 年的工作。$\alpha$ 动态不等式被定义为 delta 和 nabla 积分的线性混合，我们提出并证明了非常重要的菱形-$\alpha$一般时间尺度上的 Steffensen 型不等式。对称性在确定解决动态不等式的正确方法方面起着至关重要的作用。