Further aspects of quasi statistical convergence of sequences

In this paper, we introduce the concept of quasi statistical supremum, quasi statistical infimum of a real-valued sequence $x=(x_{k})$, and study some properties of the newly introduced notion. We also introduce the concept of quasi statistical monotonicity and establish the condition under which a quasi statistical monotonic sequence is quasi statistical convergent. We end up by giving a necessary and sufficient condition for the quasi statistical convergence of a real-valued sequence $x=(x_{k})$.