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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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 <IMG WIDTH="75" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$[J,f(x)]$"> means, regular and totally regular <!– MATH $[J,f(x,y)]$ –> <IMG WIDTH="95" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$[J,f(x,y)]$"> means, Laplace transforms in two variables
Article copyright: © Copyright 1975 American Mathematical Society