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