scholarly journals Map Ideal of Type the Domain of r -Cesàro Matrix in the Variable Exponent ℓ t . and Its Eigenvalue Distributions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Sequence Space ◽  
Variable Exponent ◽  
Topological Properties ◽  
Cesàro Matrix

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.

Fractional Cesàro Matrix and its Associated Sequence Space

2021 ◽  
Vol 8 (1) ◽  
pp. 24-39
Author(s):  
H. Roopaei ◽  
M. İlkhan
Keyword(s):  
Sequence Space ◽  
Topological Properties ◽  
Hilbert’S Inequality ◽  
Hilbert Operator ◽  
Cesàro Matrix ◽  
New Inequalities

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.

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 $(r_{1},r_{2})$-Cesàro summable sequence space of non-absolute type and the involved pre-quasi ideal

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
OM Kalthum S. K. Mohamed
Keyword(s):  
Banach Spaces ◽  
Linear Space ◽  
Sequence Space ◽  
Topological Properties ◽  
Bounded Linear ◽  
Summable Sequence ◽  
Cesàro Matrix

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 .

scholarly journals On some new modular sequence spaces

2013 ◽  
Vol 31 (2) ◽  
pp. 55 ◽  
Author(s):  
Cigdem Asma Bektas ◽  
Gülcan Atıci
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Orlicz Sequence Space ◽  
Orlicz Functions ◽  
Orlicz Sequence Spaces

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ℓM which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of ℓ (M), which is an AK-space, is the space h (M) . We define the sequence spaces ℓM (m) and ℓ N(m), where M = (Mk) and N = (Nk) are sequences of Orlicz functions such that Mk and Nk be mutually  complementary for each k. We also examine some topological properties of these spaces. We give the α−, β− and γ− duals of the sequence space h (M) and α− duals of the squence spaces ℓ (M, λ) and ℓ (N, λ).

scholarly journals The Hahn Sequence Space Defined by the Cesáro Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Murat Kirişci
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Matrix Transformations ◽  
Space Theory ◽  
Topological Properties ◽  
Cesàro Mean ◽  
First Order ◽  
Inclusion Relations ◽  
The Matrix ◽  
Cesaro Mean

The -space of all sequences is given as such that converges and is a null sequence which is called the Hahn sequence space and is denoted by . Hahn (1922) defined the space and gave some general properties. G. Goes and S. Goes (1970) studied the functional analytic properties of this space. The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by , is obtained, and some inclusion relations and some topological properties of this space are investigated. Also dual spaces of this space are computed and, matrix transformations are characterized.

scholarly journals Some Properties of the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Kuldip Raj ◽  
Sunil K. Sharma
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Topological Properties ◽  
Inclusion Relations

We introduce the sequence space defined by a Musielak-Orlicz function . We also study some topological properties and prove some inclusion relations involving this space.

scholarly journals On some topological properties of generalized difference sequence spaces

2000 ◽  
Vol 24 (11) ◽  
pp. 785-791 ◽  
Author(s):  
Mikail Et
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Difference Sequence Spaces

We obtain some topological results of the sequence spacesΔm(X), whereΔm(X)={x=(xk):(Δmxk)∈X},   (m∈ℕ), andXis any sequence space. We compute thepα-,pβ-, andpγ-duals ofl∞,c, andc0and we investigate theN-(or null) dual of the sequence spacesΔm(l∞),   Δm(c), andΔm(c0). Also we show that any matrix map fromΔm(l∞)into aBK-space which does not contain any subspace isomorphic toΔm(l∞)is compact.

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 NEW GENERALIZED CIESARO SPACE WITH SOME TOPOLOGICAL PROPERTIES

2021 ◽  
pp. 253-262
Author(s):  
Rayees Ahmad
Keyword(s):  
Sequence Space ◽  
Subject Classification ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Space

The sequence space introduced by M. Et and have studied its various properties. The aim of the present paper is to introduce the new pranormed generalized difference sequence space. and , We give some topological properties and inclusion relations on these spaces. 2010 AMS Mathematical Subject Classification: 46A45; 40C05.

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