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1995/1996 Relatively (R)-dense universal sequences for certain classes of functions
B. László, J. T. Tóth
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Real Anal. Exchange 21(1): 335-339 (1995/1996).


Let \(f:\mathbb{R} ^+\rightarrow \mathbb{R} ^+\) and \((a_n)^\infty_{n=1}\) be a sequence of positive reals. We will say that \((a_n)^\infty_{n=1}\) is relatively \((R)\)-dense for \(f\) provided that for every \(x,y\in \mathbb{R} ^+\) with \(f(x)\lt f(y)\) there exists \(n,m\in\mathbb{N} \) such that \(f(x)\lt \frac{f(a_n)}{f(a_m)}\lt f(y)\). Sufficient conditions are given for a sequence of positive reals to be relatively \((R)\)-dense for certain functions.


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B. László. J. T. Tóth. "Relatively (R)-dense universal sequences for certain classes of functions." Real Anal. Exchange 21 (1) 335 - 339, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

zbMATH: 0851.11016
MathSciNet: MR1377545

Primary: 26A99
Secondary: 11B83

Keywords: (R)-density , ratio set , sequences

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
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