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

The sequence space 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) to the space |Eϕr|(p) derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to 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. © 2018, The Author(s)