AbstractWe have constructed the sequence space $(\Xi (\zeta ,t) )_{\upsilon }$
(
Ξ
(
ζ
,
t
)
)
υ
, where $\zeta =(\zeta _{l})$
ζ
=
(
ζ
l
)
is a strictly increasing sequence of positive reals tending to infinity and $t=(t_{l})$
t
=
(
t
l
)
is a sequence of positive reals with $1\leq t_{l}<\infty $
1
≤
t
l
<
∞
, by the domain of $(\zeta _{l})$
(
ζ
l
)
-Cesàro matrix in the Nakano sequence space $\ell _{(t_{l})}$
ℓ
(
t
l
)
equipped with the function $\upsilon (f)=\sum^{\infty }_{l=0} ( \frac{ \vert \sum^{l}_{z=0}f_{z}\Delta \zeta _{z} \vert }{\zeta _{l}} )^{t_{l}}$
υ
(
f
)
=
∑
l
=
0
∞
(
|
∑
z
=
0
l
f
z
Δ
ζ
z
|
ζ
l
)
t
l
for all $f=(f_{z})\in \Xi (\zeta ,t)$
f
=
(
f
z
)
∈
Ξ
(
ζ
,
t
)
. Some geometric and topological properties of this sequence space, the multiplication mappings defined on it, and the eigenvalues distribution of operator ideal with s-numbers belonging to this sequence space have been investigated. The existence of a fixed point of a Kannan pre-quasi norm contraction mapping on this sequence space and on its pre-quasi operator ideal formed by $(\Xi (\zeta ,t) )_{\upsilon }$
(
Ξ
(
ζ
,
t
)
)
υ
and s-numbers is presented. Finally, we explain our results by some illustrative examples and applications to the existence of solutions of nonlinear difference equations.
Some Fixed Point Results in Premodular Special Space of Sequences and Their Associated Pre-Quasi-Operator Ideal