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RETRACTED: The Hausdorff measure of noncompactness for some matrix operators
Nonlinear Analysis: Theory, Methods & Applications, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohiuddine, S. A. +2 more
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Retraction notice to: ``The Hausdorff measure of noncompactness for some matrix operators''
Nonlinear Analysis: Theory, Methods & Applications, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohiuddine, S. A. +2 more
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Appl. Math. Comput., 2010
Let \(\omega \) be the space of all complex sequences \(x=\left( x_{k}\right) _{k=1}^{\infty }\), \(A=\left( a_{nk}\right) _{n,k=1}^{\infty }\) be an infinite matrix of complex numbers and \(X\) a subset of \(\omega\). The set \[ X_{A}=\left\{ x\in \omega :Ax=\sum_{k=1}^\infty a_{nk} {x_{k}}\in X\right\} \] is called the matrix domain of \(A\) in \(X\).
Ivana Djolovic, Eberhard Malkowsky
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Let \(\omega \) be the space of all complex sequences \(x=\left( x_{k}\right) _{k=1}^{\infty }\), \(A=\left( a_{nk}\right) _{n,k=1}^{\infty }\) be an infinite matrix of complex numbers and \(X\) a subset of \(\omega\). The set \[ X_{A}=\left\{ x\in \omega :Ax=\sum_{k=1}^\infty a_{nk} {x_{k}}\in X\right\} \] is called the matrix domain of \(A\) in \(X\).
Ivana Djolovic, Eberhard Malkowsky
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1984
Let \(\Omega\) be a Lebesgue-measurable subset of \({\mathbb{R}}^ n\), M(\(\Omega)\) the space of all Lebesgue-measurable functions on \(\Omega\) to \({\mathbb{R}}\) and \(T_ 0(\Omega)\) its subspace of all totally measurable functions [in the sense of \textit{N. Dunford} and \textit{J. T.
De Pascale, E., Trombetta, G.
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Let \(\Omega\) be a Lebesgue-measurable subset of \({\mathbb{R}}^ n\), M(\(\Omega)\) the space of all Lebesgue-measurable functions on \(\Omega\) to \({\mathbb{R}}\) and \(T_ 0(\Omega)\) its subspace of all totally measurable functions [in the sense of \textit{N. Dunford} and \textit{J. T.
De Pascale, E., Trombetta, G.
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Hausdorff Measures of Noncompactness and Interpolation Spaces
2016A new measure of noncompactness on Banach spaces is defined from the Hausdorff measure of noncompactness, giving a quantitative version of a classical result by R. S. Phillips. From the main result, classical results are obtained now as corollaries and we have an application to interpolation theory of Banach spaces.
da Silva, Eduardo Brandani +1 more
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2014
In this paper, we have introduced a sequence space \(l_p(r,s, t; B^{(m)})\), \(1\le p< \infty \) and proved that the space is a complete normed linear space. We have also shown that the space \(l_p(r,s, t; B^{(m)})\) is linearly isomorphic to \(l_p\) for \(1\le p< \infty \).
Amit Maji, P. D. Srivastava
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In this paper, we have introduced a sequence space \(l_p(r,s, t; B^{(m)})\), \(1\le p< \infty \) and proved that the space is a complete normed linear space. We have also shown that the space \(l_p(r,s, t; B^{(m)})\) is linearly isomorphic to \(l_p\) for \(1\le p< \infty \).
Amit Maji, P. D. Srivastava
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Minimal sets for the Hausdorff measure of noncompactness and related coefficients
Nonlinear Analysis: Theory, Methods & Applications, 2001MALUTA, ELISABETTA, S. Prus
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Hausdorff Measure of Noncompactness of Matrix Mappings on Cesàro Spaces
Boletim Da Sociedade Paranaense De Matematica, 2020Canan Hazar Güleç
exaly