Generalization of the space l(p) $l(p)$ derived by absolute Euler summability and matrix operators

Abstract

Abstract The sequence space l(p) $l(p)$ having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345–355, 1967). In the present paper, we generalize the space l(p) $l(p)$ to the space |Eϕr|(p) $\vert E_{\phi }^{r} \vert (p)$ derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to l(p) $l(p)$. Further, we determine α-, β-, and γ-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space.

Keywords

• Absolute summability
• Euler means
• Matrix transformations
• Sequences spaces