In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.

中文翻译：

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最优和非最优 Gronwall 引理

在本文中，我们研究了 Riccati 型和 Bihari 型的一些最优不等式。我们还考虑了 Wendorf 类型的非最优不等式。同时，我们得到了 IA Rus 制定的问题 5 和问题 9 的部分答案。这篇论文的动机还在于，在许多不等式中，上限不是最优的。