A sequence-to-function analogue of the Hausdorff means for double sequences: the [𝐽, 𝑓(𝑥,𝑦)] means

Ismail, Mourad El-Houssieny

doi:10.1090/S0002-9939-1975-0364942-3

A sequence-to-function analogue of the Hausdorff means for double sequences: the $[J,$ $f(x, y)]$ means
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by Mourad El-Houssieny Ismail

Proc. Amer. Math. Soc. 48 (1975), 403-408

DOI: https://doi.org/10.1090/S0002-9939-1975-0364942-3

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Abstract:

In this paper we extend the Jakimovski $[J,f(x)]$ means to double sequences. We call the new means the $[J,f(x,y)]$ means. We characterize such $f$’s that give rise to regular and to totally regular $[J,f(x,y)]$ means. We also give a necessary and sufficient condition for representability of a function $f(x,y)$ as a double Laplace transform with a determining function of bounded variation in two variables.

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