In this article, we establish sufficient conditions on the generalized Cesáro and Orlicz sequence spaces
E
such that the class
S
E
of all bounded linear operators between arbitrary Banach spaces with ...its sequence of
s
-numbers belonging to
E
generates an operator ideal. The components of
S
E
as a pre-quasi Banach operator ideal containing finite dimensional operators as a dense subset and its completeness are proved. Some inclusion relations between the operator ideals as well as the inclusion relations for their duals are obtained. Finally, we show that the operator ideal formed by
E
and approximation numbers is small under certain conditions.
In this article, we study some topological properties of the multiplication operator on Orlicz-Cesáro mean sequence spaces equipped with the pre-quasi norm and the pre-quasi operator ideal ...constructed by this sequence space and
-numbers.
In this paper, we construct and investigate the space of weighted Gamma matrix of order r in Nakano sequence space of soft functions. The idealization of the mappings has been achieved through the ...use of extended s-soft functions and this sequence space of soft functions. This new space’s topological and geometric properties, the multiplication mappings that stand in on it, and the mappings’ ideal that correspond to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated prequasi ideal. Interestingly, several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of nonlinear difference equations of soft functions are introduced.
In this article, we investigate the notion of the pre-quasi norm on a generalized Cesàro backward difference sequence space of non-absolute type
(
Ξ
(
Δ
,
r
)
)
ψ
under definite function
ψ
. We ...introduce the sufficient set-up on it to form a pre-quasi Banach and a closed special space of sequences (sss), the actuality of a fixed point of a Kannan pre-quasi norm contraction mapping on
(
Ξ
(
Δ
,
r
)
)
ψ
, it supports the property (R) and has the pre-quasi normal structure property. The existence of a fixed point of the Kannan pre-quasi norm nonexpansive mapping on
(
Ξ
(
Δ
,
r
)
)
ψ
and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by
(
Ξ
(
Δ
,
r
)
)
ψ
and
s
-numbers has been determined. Finally, we support our results by some applications to the existence of solutions of summable equations and illustrative examples.
In this paper, we investigate the necessary conditions on any
s
-type sequence space to form an operator ideal. As a result, we show that the
s
-type Nakano generalized difference sequence space
X
...fails to generate an operator ideal. We investigate the sufficient conditions on
X
to be premodular Banach special space of sequences and the constructed prequasi-operator ideal becomes a small, simple, and closed Banach space and has eigenvalues identical with its
s
-numbers. Finally, we introduce necessary and sufficient conditions on
X
explaining some topological and geometrical structures of the multiplication operator defined on
X
.
In general, we have constructed the operator ideal generated by extended s-fuzzy numbers and a certain space of sequences of fuzzy numbers. An investigation into the conditions sufficient for ...variable exponent Cesàro sequence space of fuzzy functions furnished with the definite function to create pre-quasi-Banach and closed is carried out. The R and the normal structural properties of this space are shown. Fixed points for Kannan contraction and nonexpansive mapping have been introduced. Lastly, we explore whether the Kannan contraction mapping has a fixed point in its associated pre-quasioperator ideal. The existence of solutions to nonlinear difference equations is illustrated with a few real-world examples and applications.
Consider the space of weighted binomial matrices in the Nakano sequence space of soft functions. We have offered some geometric and topological structures of the multiplication operator acting on ...this space and its associated operator ideal. The existence of a fixed point of the Kannan contraction operator in this prequasioperator ideal is confirmed. Finally, we discuss many applications of solutions to nonlinear stochastic dynamical matrix systems and illustrative examples of our findings.
The Orlicz function-defined sequence spaces of functions by relative uniform convergence of sequences related to p-absolutely summable spaces are a new concept that is introduced in this article. We ...look at its various attributes, such as solidity, completeness, and symmetry. We also look at a few insertional connections involving these spaces.
We developed the operators ideal in this article by extending s-soft reals and a particular space of sequences with soft real numbers. The criteria necessary for the Nakano sequence space of soft ...real numbers given with the definite function to be prequasi Banach and closed are investigated. This space’s (R) and normal structural features are illustrated. Fixed points have been introduced for Kannan contraction and nonexpansive mapping. Finally, we investigate whether the Kannan contraction mapping has a fixed point in the prequasi operator ideal with which it is linked. By examining some real-world instances and their applications, it is demonstrated that there exist solutions to nonlinear difference equations.
Some topological and geometric behavior of the space of all sequences whose generalized mean transforms are in Nakano sequence space, the multiplication mappings acting on it, and the eigenvalue ...distribution of mappings ideal generated by this space and
s
-numbers are discussed. We construct the existence of a fixed point of Kannan contraction mapping on these spaces. Several numerical experiments are presented to illustrate our results. Moreover, some successful applications to the existence of solutions of nonlinear difference equations are explained. The strength here is that the current results are constructed under flexible setups given by controlling the weight and power of these spaces.
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