On some imbedding relations between certain sequence spaces

Abstract

In the present paper, we introduce the sequence space $l^{\lambda}_p$ of non-absolute type which is a $p$-normed space and a $BK$-space in the cases of $0 < p < 1$ and $0 < p < 1$ i $1 \leq p < \infty$, respectively. Further, we derive some imbedding relations and construct the basis for the space $l^{\lambda}_p$, where $1 \leq p < \infty$.