We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization of approximation spaces which arise from sparse approximation or have applications to interpolation theory. An elementary proof of a constant in the strong discrete Stechkin inequality given by Bennett is provided, and we improve the constants given by Levin and Stechkin and by Copson. Finally, the minimal constants in the weak discrete Stechkin inequalities and both continuous Stechkin inequalities are presented.

翻译：我们解决了强弱的STTEKIN不平等中的最佳常数,包括离散的和连续的变体。这些不平等表现在对近似空间的定性中,这些近似空间是因近似稀少产生的,或适用于内插理论。 我们提供了一份基本证据,证明Bennett给出的离散的Stechkin高度不平等中的常数。 我们改善了Levin和STTEKkin以及Copson给出的常数。 最后,提出了弱弱离散的STTEKIN不平等中最小的常数以及持续的STechkin不平等。