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 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 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 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 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.

Construction of fixed point operators for nonlinear difference equations of non integer order with impulses

2020 ◽  
Vol 23 (3) ◽  
pp. 886-907
Author(s):  
Syed Sabyel Haider ◽  
Mujeeb Ur Rehman
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Nonlinear Difference Equations ◽  
Fractional Difference ◽  
Integer Order ◽  
Fractional Difference Equation ◽  
Point Operator

AbstractIn this article, we establish a technique for transforming arbitrary real order delta difference equations with impulses to corresponding summation equations. The technique is applied to non-integer order delta difference equation with some boundary conditions. Furthermore, the summation formulation for impulsive fractional difference equation is utilized to construct fixed point operator which in turn are used to discuss existence of solutions.

scholarly journals On the well posed solutions for nonlinear second order neutral difference equations

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Marek Galewski ◽  
Ewa Schmeidel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Main Tool ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Neutral Difference Equations ◽  
Darbo Fixed Point Theorem ◽  
Well Posed

AbstractIn this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.

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 Dynamic equations x(Δm)(t) = f(t, x(t)) on time scales

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Aneta Sikorska-Nowak
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Dynamic Equations ◽  
Sadovskii Fixed Point Theorem

AbstractIn this paper we prove the existence of solutions and Carathéodory’s type solutions of the dynamic Cauchy problemThe Sadovskii fixed point theorem and Ambrosetti’s lemma are used to prove the main result.As dynamic equations are an unification of differential and difference equations our result is also valid for differential and difference equations. The results presented in this paper are new not only for Banach valued functions but also for real valued functions.

Dynamics and bifurcations of a host–parasite model

2017 ◽  
Vol 10 (06) ◽  
pp. 1750089 ◽  
Author(s):  
Ali Atabaigi ◽  
Mohammad Hossein Akrami
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Parameter Family ◽  
Invariant Curve ◽  
Discrete Models ◽  
Nonlinear Difference Equations ◽  
Host Parasite ◽  
Parameter Values ◽  
Two Parameter

A two-parameter family of discrete models, consisting of two coupled nonlinear difference equations, describing a host–parasite interaction is considered. In particular, we prove that the model has at most one nontrivial interior fixed point which is stable for a certain range of parameter values and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter.

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.

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