On $\Delta$-quasi-slowly oscillating sequences

Abstract

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.

This paper has been withdrawn by the author due to the publication in the journal, Computer and Mathematics with Applications