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

Author: Mourad El-Houssieny Ismail
Journal: Proc. Amer. Math. Soc. 48 (1975), 403-408
MSC: Primary 40G05
MathSciNet review: 0364942
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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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Keywords: Jakimovski's $ [J,f(x)]$ means, regular and totally regular $ [J,f(x,y)]$ means, Laplace transforms in two variables
Article copyright: © Copyright 1975 American Mathematical Society

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