scholarly journals Hausdorff measure of noncompactness of matrix operators on some new difference sequence spaces

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Elahe Abyar ◽  
Mohammad Bagher Ghaemi
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Hausdorff Measure Of Noncompactness ◽  
Matrix Operators ◽  
Difference Sequence Spaces

On difference sequence spaces of fractional-order involving Padovan numbers

2020 ◽  
pp. 2150095
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Syed Abdul Mohiuddine
Keyword(s):  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Hausdorff Measure Of Noncompactness ◽  
Order Difference ◽  
Matrix Formula ◽  
Difference Sequence Spaces

In this paper, we introduce Padovan difference sequence spaces of fractional-order [Formula: see text] [Formula: see text] [Formula: see text] by the composition of the fractional-order difference operator [Formula: see text] and the Padovan matrix [Formula: see text] defined by [Formula: see text] and [Formula: see text] respectively, where the sequence [Formula: see text] is the Padovan sequence. We give some topological properties, Schauder basis and [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the newly defined spaces. We characterize certain matrix classes related to the [Formula: see text] space. Finally, we characterize certain classes of compact operators on [Formula: see text] using Hausdorff measure of noncompactness.

scholarly journals Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mursaleen ◽  
A. Latif
Keyword(s):  
Hausdorff Measure ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Hausdorff Measure Of Noncompactness ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Matrix Operators

We determine the conditions for some matrix transformations fromn(ϕ), where the sequence spacen(ϕ), which is related to theℓpspaces, was introduced by Sargent (1960). We also obtain estimates for the norms of the bounded linear operators defined by these matrix transformations and find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

scholarly journals Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5459-5470
Author(s):  
Ishfaq Malik ◽  
Tanweer Jalal
Keyword(s):  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper we first introduce N?q?summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c,c0, and l?. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

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