cesàro matrix
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2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hadi Roopaei

AbstractIn this paper, we introduce two factorizations for the Cesàro matrix of order n based on Cesàro and gamma matrices. The results of these factorizations are new inequalities, one of which is a generalized version of the well-known Hardy’s inequality. Moreover, we obtain the norm of Cesàro operator of order n on Cesàro and gamma matrix domains.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed

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.


Positivity ◽  
2021 ◽  
Author(s):  
Chikkanna R. Selvaraj ◽  
Suguna Selvaraj
Keyword(s):  

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Awad A. Bakery ◽  
M. H. El Dewaik

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed

In this article, we define a new sequence space generated by the domain of r -Cesàro matrix in Nakano sequence space. Some geometric and topological properties of this sequence space, the multiplication maps defined on it, and the eigenvalue distributions of map ideal with s -numbers that belong to this sequence space have been examined.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed

AbstractWe suggest a sufficient setting on any linear space of sequences $\mathcal{V}$ V such that the class $\mathbb{B}^{s}_{\mathcal{V}}$ B V s of all bounded linear mappings between two arbitrary Banach spaces with the sequence of s-numbers in $\mathcal{V}$ V constructs a map ideal. We define a new sequence space $(\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }$ ( ces r 1 , r 2 t ) υ for definite functional υ by the domain of $(r_{1},r_{2})$ ( r 1 , r 2 ) -Cesàro matrix in $\ell _{t}$ ℓ t , where $r_{1},r_{2}\in (0,\infty )$ r 1 , r 2 ∈ ( 0 , ∞ ) and $1\leq t<\infty $ 1 ≤ t < ∞ . We examine some geometric and topological properties of the multiplication mappings on $(\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }$ ( ces r 1 , r 2 t ) υ and the pre-quasi ideal $\mathbb{B}^{s}_{ (\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }}$ B ( ces r 1 , r 2 t ) υ s .


2021 ◽  
Vol 8 (1) ◽  
pp. 24-39
Author(s):  
H. Roopaei ◽  
M. İlkhan

Abstract In this research, we introduce a new fractional Cesàro matrix and investigate the topological properties of the sequence space associated with this matrix.We also introduce a fractional Gamma matrix aswell and obtain some factorizations for the Hilbert operator based on Cesàro and Gamma matrices. The results of these factorizations are two new inequalities one ofwhich is a generalized version of thewell-known Hilbert’s inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.


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