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.
Eigenvalues of s-Type Operators on Prequasi Normed Ct,p