Results 101 to 110 of about 165,965,242 (115)

The Hausdorff measure of noncompactness of operators on the matrix domains of triangles in the spaces of strongly summable and bounded sequences

Applied Mathematics and Computation, 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 Djolović, Eberhard Malkowsky
openaire   +3 more sources

Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means [PDF]

Computers and Mathematics With Applications, 2011
For a sequence x=(xk), we denote the difference sequence by Δx=(xk−xk−1). Let u=(uk)k=0∞ and v=(vk)k=0∞ be the sequences of real numbers such that uk≠0, vk≠0 for all k∈N.
Harun Polat, M Mursaleen, Vatan Karakaya   +2 more
exaly   +2 more sources

A compactness criterion and the Hausdorff measure of noncompactness for subsets of the space of measurable functions

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.
openaire   +2 more sources

Hausdorff Measures of Noncompactness and Interpolation Spaces

2016
A 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, Fernanadez, Dicesar L.   +1 more
openaire   +1 more source

Applications of the Hausdorff Measure of Noncompactness on the Space $$l_p(r,s, t; B^{(m)})$$, $$1\le p< \infty $$

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
openaire   +1 more source

Existence of solution of infinite systems of singular integral equations of two variables in C(I x I, l(p)) with I = [0, T], T > 0 and 1 < p < infinity using Hausdorff measure of noncompactness

2023
3023
Das, A., Hazarika, B., Sadarangani Sadarangani, Kishin Bhagwands   +2 more
openaire   +1 more source

On matrix transformations and Hausdorff measure of noncompactness of Euler difference sequence spaces of fractional order

Quaestiones Mathematicae, 2020
Uğur Kadak, P Baliarsingh
exaly  

Noncompactness of Segments in the Gromov–Hausdorff Space

Moscow University Mathematics Bulletin, 2022
exaly  

On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions

Nonlinear Analysis: Theory, Methods & Applications, 1983
Hans-Peter Heinz
exaly  

Some fixed point theorems for s-convex subsets in p-normed spaces based on measures of noncompactness

Journal of Fixed Point Theory and Applications, 2018
Jianzhong Xiao
exaly