Abstract
In this article we introduce paranormed Nörlund difference sequence space of fractional order α, Nt
(p, Δ(α)) defined by the composition of fractional difference operator Δ(α), defined by
(
Δ
(
α
)
x
)
k
=
∑
i
=
0
∞
(
−
1
)
i
Γ
(
α
+
1
)
i
!
Γ
(
α
−
i
+
1
)
x
k
−
i
,
$\begin{array}{}
\displaystyle
(\Delta^{(\alpha)}x)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i},
\end{array}$
and Nörlund matrix Nt
. We give some topological properties, obtain the Schauder basis and determine the α−, β− and γ-duals of the new space. We characterize certain matrix classes related to this new space. Finally we investigate certain geometric properties of the space Nt
(p, Δ(α)).