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 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 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.

Modified CQ-Algorithms for G-Nonexpansive Mappings in Hilbert Spaces Involving Graphs

2020 ◽  
Vol 16 (01) ◽  
pp. 89-103
Author(s):  
W. Cholamjiak ◽  
D. Yambangwai ◽  
H. Dutta ◽  
H. A. Hammad
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Iterative Schemes ◽  
Cq Method

In this paper, we introduce four new iterative schemes by modifying the CQ-method with Ishikawa and [Formula: see text]-iterations. The strong convergence theorems are given by the CQ-projection method with our modified iterations for obtaining a common fixed point of two [Formula: see text]-nonexpansive mappings in a Hilbert space with a directed graph. Finally, to compare the rate of convergence and support our main theorems, we give some numerical experiments.

scholarly journals A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 123
Author(s):  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Fixed Point Algorithm ◽  
Mann Algorithm

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel’skiǐ fixed point algorithm than with the modified Krasnosel’skiǐ–Mann algorithm.

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 An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery

2022 ◽  
Vol 7 (2) ◽  
pp. 1775-1790
Author(s):  
Nipa Jun-on ◽  
◽  
Raweerote Suparatulatorn ◽  
Mohamed Gamal ◽  
Watcharaporn Cholamjiak ◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Signal Recovery ◽  
Numerical Examples ◽  
Different Types ◽  
Lasso Problem ◽  
Inertial Technique

<abstract><p>This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.</p></abstract>

scholarly journals A note on Nakano generalized difference sequence space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
Afaf R. Abou Elmatty
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Operator Ideal ◽  
Difference Sequence ◽  
Geometrical Structures ◽  
Difference Sequence Space ◽  
Necessary And Sufficient ◽  
Special Space ◽  
Type Sequence

Abstract 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.

Radius vs diameter

2018 ◽  
pp. 102-115
Author(s):  
Kazimierz Goebel ◽  
Stanisław Prus
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Main Tool ◽  
Normal Structure ◽  
Point Theory ◽  
The Subject ◽  
The Relationship ◽  
Bounded Sets

The subject of the chapter is the relationship between the (Chebyshev) radius and diameter of convex bounded sets. The main tool is the Jung coefficient. Diametral sets and normal structure in connection with the fixed point theory for nonexpansive mappings are presented.

scholarly journals Common fixed points for generalized asymptotically nonexpansive mappings

2012 ◽  
Vol 44 (1) ◽  
pp. 23-29
Author(s):  
Sumit Chandok ◽  
T. D. Narang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Asymptotically Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
The Subject ◽  
Common Fixed Point Theorem

A common fixed point theorem for noncommuting generalized asymptotically nonexpansive mappings has been obtained in convex metric spaces. As an application, a result on the set of best approximation is also derived for such class of mappings. The proved results unify and extend some of the known results on the subject.

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