Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference34 articles.
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2. Faried, N., Bakery, A.A.: Small operator ideals formed by s numbers on generalized Cesàro and Orlicz sequence spaces. J. Inequal. Appl. 2018(1), 357 (2018). https://doi.org/10.1186/s13660-018-1945-y
3. Pietsch, A.: Operator Ideals. North-Holland, Amsterdam (1980)
4. Pietsch, A.: Small ideals of operators. Stud. Math. 51, 265–267 (1974)
5. Makarov, B.M., Faried, N.: Some properties of operator ideals constructed by s numbers (in Russian). In: Theory of Operators in Functional Spaces. Academy of Science, Novosibirsk, pp. 206–211 (1977)
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