On some characterizations of $\Delta$-deferred weighted statistical boundedness On some characterizations of statistical boundedness

Abstract

In this article, we intend to extend the investigation for statistical boundedness of sequences and study $\Delta$-deferred Cesàro and deferred Riesz statistical bounded sequences of order $\gamma$. Some interesting inclusion relations are presented. Further, with the aid of interesting examples, we investigate some relationships among these concepts. Some characterizations of $\Delta$-deferred weighted statistical boundedness are developed in this paper. Finally, we apply the notion of $\Delta$-deferred weighted statistical boundedness with a view to prove the decomposition theorem.