scholarly journals Some Fixed Point Results of Kannan Maps on the Nakano Sequence Space

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Awad A. Bakery ◽  
O. M. Kalthum S. K. Mohamed
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Sequence Space ◽  
Numerical Experiments ◽  
Variable Exponent ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Recent Past ◽  
Fatou Property ◽  
Kannan Contraction

In the recent past, some researchers studied some fixed point results on the modular variable exponent sequence space ℓ r . ψ , where ψ v = ∑ a = 0 ∞ 1 / r a v a r a and r a ≥ 1 . They depended on their proof that the modular ψ has the Fatou property. But we have explained that this result is incorrect. Hence, in this paper, the concept of the premodular, which generalizes the modular, on the Nakano sequence space such as its variable exponent in 1 , ∞ and the operator ideal constructed by this sequence space and s -numbers is introduced. We construct the existence of a fixed point of Kannan contraction mapping and Kannan nonexpansive mapping acting on this space. It is interesting that several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of summable equations are introduced. The novelty lies in the fact that our main results have improved some well-known theorems before, which concerned the variable exponent in the aforementioned space.

scholarly journals Kannan Contraction Operator on the Domain of r . -Cesàro Matrix in ℓ t . and Related Prequasi Ideal with an Application of Nonlinear Difference Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Awad A. Bakery ◽  
M. H. El Dewaik
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Sequence Space ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Operator Ideal ◽  
Nonlinear Difference Equations ◽  
Cesàro Matrix ◽  
Eigenvalues Distribution ◽  
Kannan Contraction

In this article, the sequence space Ξ r , t υ has been built by the domain of r l -Cesàro matrix in Nakano sequence space ℓ t l , where t = t l and r = r l are sequences of positive reals with 1 ≤ t l < ∞ , and υ f = ∑ l = 0 ∞ ∑ z = 0 l r z f z / ∑ z = 0 l r z t l , with f = f z ∈ Ξ r , t . Some topological and geometric behavior of Ξ r , t υ , the multiplication maps acting on Ξ r , t υ , and the eigenvalues distribution of operator ideal constructed by Ξ r , t υ and s -numbers have been examined. The existence of a fixed point of Kannan prequasi norm contraction mapping on this sequence space and on its prequasi operator ideal are investigated. Moreover, we indicate our results by some explanative examples and actions to the existence of solutions of nonlinear difference equations.

scholarly journals Some Fixed Point Results in Premodular Special Space of Sequences and Their Associated Pre-Quasi-Operator Ideal

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Awad A. Bakery ◽  
Elsayed A. E. Mohamed ◽  
O. M. Kalthum S. K. Mohamed
Keyword(s):  
Fixed Point ◽  
Sequence Space ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Operator Ideal ◽  
The Subject ◽  
Special Space ◽  
Kannan Contraction

A weighted Nakano sequence space and the s -numbers it contains are the subject of this article, which explains the concept of the pre-quasi-norm and its operator ideal. We show that both Kannan contraction and nonexpansive mappings acting on these spaces have a fixed point. A slew of numerical experiments back up our findings. The presence of summable equations’ solutions is shown to be useful in a number of ways. Weight and power of the weighted Nakano sequence space are used to define the parameters for this technique, resulting in customizable solutions.

scholarly journals Solutions of nonlinear difference equations in the domain of $(\zeta _{n})$-Cesàro matrix in $\ell _{t(\cdot)}$ of nonabsolute type, and its pre-quasi ideal

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Sequence Space ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Operator Ideal ◽  
Topological Properties ◽  
Nonlinear Difference Equations ◽  
Cesàro Matrix ◽  
Eigenvalues Distribution

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.

scholarly journals Nonexpansive Mappings on New Premodular Special Space of Sequences

2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Fixed Point ◽  
Sequence Space ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Operator Ideal ◽  
Orlicz Sequence Space ◽  
Practical Applications ◽  
Special Space ◽  
Kannan Contraction

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.

scholarly journals The Opial condition in variable exponent sequence spaces with applications

2019 ◽  
Vol 35 (3) ◽  
pp. 273-279
Author(s):  
MOSTAFA BACHAR ◽  
◽  
MOHAMED A. KHAMSI ◽  
MESSAOUD BOUNKHEL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Sequence Space ◽  
Variable Exponent ◽  
Sequence Spaces ◽  
Opial Condition ◽  
Opial Property

In this work, we show an analogue to the Opial property for the coordinate-wise convergence in the variable exponent sequence space. This property allows us to prove a fixed point theorem for the mappings which are nonexpansive in the modular sense.

scholarly journals Existence of Solutions for Integrodifferential Equations of Fractional Order with Antiperiodic Boundary Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Integrodifferential Equations ◽  
Krasnoselskii’S Fixed Point Theorem

We discuss the existence of solutions for a nonlinear antiperiodic boundary value problem of integrodifferential equations of fractional orderq∈(1,2]. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to establish the results.

scholarly journals Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions

2018 ◽  
Vol 23 (3) ◽  
pp. 36 ◽  
Author(s):  
Hamed Bazgir ◽  
Bahman Ghazanfari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Local Boundary ◽  
New Class ◽  
Non Local

In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results.

scholarly journals Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 270
Author(s):  
Pheak Neang ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Given

In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.

scholarly journals The Kannan Contraction Mapping Theorem for Composition Operators in Metric Spaces and Partially Ordered Metric Spaces

2019 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Composition Operators ◽  
Contraction Mapping Theorem ◽  
Ordered Metric Spaces ◽  
Kannan Contraction

In this paper, fixed point theorems of the Kannan type are obtained in the setting of metric space and metric space endowed with partial order, respectively, for self-mappings that are composition operators.

Existence of solutions of cantilever beam problem via (α-β-FG)-contractions in b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3057-3074 ◽  
Author(s):  
Hemant Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Periodic Point ◽  
Cantilever Beam ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Sufficient Conditions

In this work, our intention is to introduce the notion of rational (?-?-FG)-contraction mapping in b-metric-like spaces, and produce relevant fixed point and periodic point results for weakly ?-admissible mappings. Ulam-Hyers stability of this problem is also investigated. To illustrate our results, we give throughout the paper some examples, in particular in order to justify the use of rational terms. As an application, we obtain sufficient conditions for the existence of solutions for Cantilever Beam Problem.

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