On $Δ$-quasi-slowly oscillating sequences

Details On $Δ$-quasi-slowly oscillating sequences On $Δ$-quasi-slowly oscillating sequences

2011-02-16

arxiv.org/abs/1102.3293v2

Mathematics

Functional Analysis

This paper has been withdrawn by the author due to the publication in the journal, Computer and Mathematics with Applications

Scientific paper

A sequence $(x_{n})$ of points in a topological group is called $\Delta$-quasi-slowly oscillating if $(\Delta x_{n})$ is quasi-slowly oscillating, and is called quasi-slowly oscillating if $(\Delta x_{n})$ is slowly oscillating. A function $f$ defined on a subset of a topological group is quasi-slowly (respectively, $\Delta$-quasi-slowly) oscillating continuous if it preserves quasi-slowly (respectively, $\Delta$-quasi-slowly) oscillating sequences, i.e. $(f(x_{n}))$ is quasi-slowly (respectively, $\Delta$-quasi-slowly) oscillating whenever $(x_{n})$ is. We study these kinds of continuities, and investigate relations with statistical continuity, lacunary statistical continuity, and some other types of continuities in metrizable topological groups.

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