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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0364942-3
PII: S 0002-9939(1975)0364942-3
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