[l(p)](e.r) Euler-riesz difference sequence spaces

Abstract

Baar and Braha [1], introduced the sequence spaces l(infinity), C and C-0 of Euler- Cesaro bounded, convergent and null difference sequences and studied their somere properties. Then, in [2], we introduced the sequence spaces [l(infinity)] and [c](e.r) and [c(0)](e.r), of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean E-1 and Riesz mean R-q with backward difference operator Delta. The main purpose of this study is to introduce the sequence space [l(p)](e.r), of Euler-Riesz p absolutely convergent series, where 1 <= p < infinity, difference sequences by using the composition of the Euler mean El and Riesz mean R-q with backward difference operator Delta. Furthermore, the inclusion l(p) subset of [(p)](e.r), hold, the basis of the sequence space [l(p)](e.r) is constucted and alpha, -beta- and gamma- duals of the space are determined. Finally, the classes of matrix transformations from the [l(p)](e.r) Euler-Riesz difference sequence space to the spaces l(infinity),,c and c(0) are characterized. We devote the final section of the paper to "examine some geometric properties of the space [l(p)](e.r.)