scholarly journals Approximation of lower bound for matrix operators on the weighted sequence space $C_{p}^r(w)(p \in (0,1))$

2015 ◽  
Vol 6 (3) ◽  
pp. 203-215 ◽  
Author(s):  
Gholamreza Talebi ◽  
Hossein Salmei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Weighted Sequence ◽  
Matrix Operators ◽  
Weighted Sequence Space

Weighted bounded solutions for a class of nonlinear fractional equations

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Carlos Lizama ◽  
M. Pilar Velasco
Keyword(s):  
Fixed Point ◽  
Sequence Space ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Bounded Solutions ◽  
Theoretical Methods ◽  
Fractional Equations ◽  
Weighted Sequence ◽  
Vector Valued ◽  
Weighted Sequence Space

AbstractLeton the vector-valued weighted sequence spaceOur analysis relies on the fixed point theory and operator-theoretical methods.

scholarly journals A study on Copson operator and its associated sequence space II

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Domains

AbstractIn this paper, we investigate some properties of the domains $c(C^{n})$ c ( C n ) , $c_{0}(C^{n})$ c 0 ( C n ) , and $\ell _{p}(C^{n})$ ℓ p ( C n ) $(0< p<1)$ ( 0 < p < 1 ) of the Copson matrix of order n, where c, $c_{0}$ c 0 , and $\ell _{p}$ ℓ p are the spaces of all convergent, convergent to zero, and p-summable real sequences, respectively. Moreover, we compute the Köthe duals of these spaces and the lower bound of well-known operators on these sequence spaces. The domain $\ell _{p}(C^{n})$ ℓ p ( C n ) of Copson matrix $C^{n}$ C n of order n in the sequence space $\ell _{p}$ ℓ p , the norm of operators on this space, and the norm of Copson operator on several matrix domains have been investigated recently in (Roopaei in J. Inequal. Appl. 2020:120, 2020), and the present study is a complement of our previous research.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

scholarly journals Compact matrix operators on a new sequence space related to ℓ p $\ell_{p}$ spaces

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Abdullah Alotaibi ◽  
Mohammad Mursaleen ◽  
Syed Abdul Mohiuddine
Keyword(s):  
Sequence Space ◽  
Matrix Operators
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