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.
The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals ...that the idea has only been examined for crisp mappings in either symmetric or asymmetric spaces. Hence, the aim of this paper is to introduce the notion of invariant points for non-crisp set-valued mappings in metric-like spaces. To this effect, the technique of κ-contraction and Feng-Liu’s approach are combined to establish new versions of intuitionistic fuzzy functional equations. One of the distinguishing ideas of this article is the study of fixed point theorems of intuitionistic fuzzy set-valued mappings without using the conventional Pompeiu–Hausdorff metric. Some of our obtained results are applied to examine their analogues in ordered metric-like spaces endowed with an order and binary relation as well as invariant point results of crisp set-valued mappings. By using a comparative example, it is observed that a few important corresponding notions in the existing literature are complemented, unified and generalized.
We suggest a sufficient setting on any linear space of sequences
V
such that the class
B
V
s
of all bounded linear mappings between two arbitrary Banach spaces with the sequence of
s
-numbers in
V
...constructs a map ideal. We define a new sequence space
(
ces
r
1
,
r
2
t
)
υ
for definite functional
υ
by the domain of
(
r
1
,
r
2
)
-Cesàro matrix in
ℓ
t
, where
r
1
,
r
2
∈
(
0
,
∞
)
and
1
≤
t
<
∞
. We examine some geometric and topological properties of the multiplication mappings on
(
ces
r
1
,
r
2
t
)
υ
and the pre-quasi ideal
B
(
ces
r
1
,
r
2
t
)
υ
s
.
In the framework of complete metric spaces, the major objective of this paper is to investigate if a common coincidence point exists for more than two fuzzy mappings meeting the criteria of hybrid ...fuzzy contractions of Nadler’s type in connection with the Hausdorff metric. Fascinating examples are also provided to show how the strategy can be used. For the presence of a common
α
-fuzzy fixed point of three and four fuzzy mappings, we have derived sufficient requirements. Further prior observations are offered as corollaries from the relevant literature. Some implications that are clear in this mode and widely covered in literature are expanded upon and included in our study.
In this manuscript, a new family of contractions called Jaggi-type hybrid G−ϕ-contraction is introduced and some fixed point results in generalized metric space that are not deducible from their akin ...in metric space are obtained. The preeminence of this class of contractions is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, several corollaries that reduce our result to other well-known results in the literature are highlighted and analyzed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for the solution of a family of integral equations.
In this paper, we construct and investigate the space of null variable exponent second-order quantum backward difference sequences of fuzzy functions, which are crucial additions to the concept of ...modular spaces. The idealization of the mappings has been achieved through the use of extended s− fuzzy functions and this sequence space of fuzzy functions. This new space’s topological and geometric properties and the mappings’ ideal that corresponds to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated pre-quasi ideal. To demonstrate our findings, we give a number of numerical experiments. There are also some significant applications of the existence of solutions to nonlinear difference equations of fuzzy functions.
Among various efforts in advancing fuzzy mathematics, a lot of attentions have been paid to examine novel intuitionistic fuzzy analogues of the classical fixed point results. Along this direction, ...the idea of intuitionistic fuzzy mapping (IFM) is used in this paper to establish some fixed point (FP) results in complex-valued b-metric spaces. Moreover, from application perspective, one of our results is rendered to provide an existence condition for a solution of Caputo-type fractional differential equations. A few nontrivial illustrations are also furnished to authenticate and indicate the usability of the presented results.
For different premodular, which is a generalization of modular, defined by weighted Orlicz sequence space and its prequasi operator ideal, we have examined the existence of a fixed point for both ...Kannan contraction and nonexpansive mappings acting on these spaces. Some numerous numerical experiments and practical applications are presented to support our results.
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.
In this article, the necessary conditions on s-type Orlicz generalized difference sequence space to generate an operator ideal have been examined. Therefore, the s-type Orlicz generalized difference ...sequence space which fails to generate an operator ideal has been shown. We investigate the sufficient conditions on this sequence space to be premodular Banach special space of sequences, and the constructed pre-quasi operator ideal becomes small, simple, closed, Banach space and has eigenvalues identical with its s-numbers.
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