Measures of affinity of a sequence for a number

Authors: Nuray, Fatih; Ruckle, William H.

Source: Quaestiones Mathematicae, Volume 25, Number 4, 1 December 2002 , pp. 473-481(9)

Publisher: NISC Pty Ltd

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Abstract:

We define strong and weak affinities of a number a for a sequence (x_k) denoted by L (a,(x_k)) and U (a, (x_k)) respectively. We show U (a,(x_k)) > 0 if and only if the number a is a statistical limit point of the sequence (x_k). We consider the distribution of sequences with positive weak and strong measures of affinity within the space l^∞ of bounded sequences. The main result is that the set of bounded sequences with U (a,(x_k)) > 0, that is, the set of sequences with statistical limit points, is a dense subset in l^∞ of the first category. We also show the set of sequences with positive strong affinities is a nowhere dense subset of l^∞.

Keywords: STATISTICAL CONVERGENCE; STATISTICAL LIMIT POINT

Document Type: Research article

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