scholarly journals Hausdorff measure of noncompactness in some sequence spaces of a triple band matrix

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Ali Karaisa
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sequence Spaces ◽  
Hausdorff Measure Of Noncompactness ◽  
Band Matrix ◽  
Triple Band

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 New approach to some results related to mixed norm sequence spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 83-88 ◽  
Author(s):  
Ivana Djolovic ◽  
Eberhard Malkowsky ◽  
Katarina Petkovic
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Diagonal Matrix ◽  
Sequence Spaces ◽  
Mixed Norm ◽  
Hausdorff Measure Of Noncompactness ◽  
Infinite Matrices ◽  
New Approach ◽  
The Subject ◽  
Bk Spaces

In this paper, the mixed norm sequence spaces ?p,q for 1 ? p,q ? ? are the subject of our research; we establish conditions for an operator T? to be compact, where T? is given by a diagonal matrix. This will be achieved by applying the Hausdorff measure of noncompactness and the theory of BK spaces. This problem was treated and solved in [5, 6], but in a different way, without the application of the theory of infinite matrices and BK spaces. Here, we will present a new approach to the problem. Some of our results are known and others are new.

scholarly journals Measure of noncompactness of operators and matrices on the spacescandc0

2006 ◽  
Vol 2006 ◽  
pp. 1-5 ◽  
Author(s):  
Bruno De Malafosse ◽  
Eberhard Malkowsky ◽  
Vladimir Rakocevic
Keyword(s):  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Necessary And Sufficient

In this note, using the Hausdorff measure of noncompactness, necessary and sufficient conditions are formulated for a linear operator and matrices between the spacescandc0to be compact. Among other things, some results of Cohen and Dunford are recovered.

scholarly journals Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey
Keyword(s):  
Banach Space ◽  
Mild Solution ◽  
Hausdorff Measure ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Existence Results ◽  
Hausdorff Measure Of Noncompactness ◽  
Arbitrary Banach Space ◽  
Fractional Integrodifferential Equation

We consider an impulsive neutral fractional integrodifferential equation with infinite delay in an arbitrary Banach spaceX. The existence of mild solution is established by using solution operator and Hausdorff measure of noncompactness.

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