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math.CA2017
The Abel-Steffensen inequality in higher dimensions
Constantin P. Niculescu
The Abel-Steffensen inequality is extended to the context of several variables. Applications to Fourier analysis of several variables and Riemann-Stieltjes integration are also inc…
math.CA2017
A note on Abel's partial summation formula
Constantin P. Niculescu, Marius Marinel Stănescu
Several applications of Abel's partial summation formula to the convergence of series of positive vectors are presented. For example, when the norm of the ambient ordered Banach sp…