Applied Mathematics & Information Sciences

Author Country (or Countries)

Saudi Arabia


We deal with a complete normed space $E$, a scalar sequence space $\lambda$, and an Orlicz mapping $M$ to introduce and study some properties of the spaces $\lambda_M\{E\}$ of all $E-$valued sequences that are absolutely $(\lambda, M)$-summable. Denote by $\lambda_M\{E\}_{r}$ the subspace of $\lambda_M\{E\}$ whose elements are AK-sequences. We describe the continuous linear forms on this space in term of $E^*-$valued sequences that are absolutely $(\lambda^*, N)$-summable, where $N$ is the Orlicz mapping complement of $M$.

Digital Object Identifier (DOI)