Measure of weak noncompactness - Open Access .click

Annali Di Matematica Pura Ed Applicata, 1988
The authors give an axiomatic definition of measures of weak noncompactness which is in some sense parallel to \textit{B. N. Sadovskij}'s definition of measures of (strong) noncompactness [see e.g. Usp. Mat. Nauk 27, No.1, 81-146 (1972; Zbl 0243.47033)]. The first explicit measure of weak noncompactness is due to \textit{F. S. de Blasi} [Bull.
Józef Banas, Banas Józef
exaly +2 more sources

Measure of super weak noncompactness in some Banach sequence spaces

Journal of Mathematical Analysis and Applications, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kun Tu
exaly +3 more sources

A Measure of Weak Noncompactness in $$L^1({\mathbb {R}}^N)$$ and Applications

Mediterranean Journal of Mathematics, 2022
A new measure of weak noncompactness in the Banach space $L^1(\mathbb{R}^N)$ is proposed. It is a generalization of the Banas-Knap measure of weak noncompactness, which in turn is a generalization of the De Blasi measure of weak noncompactness. Then, the multidimensional nonlinear functional integral equation \[ u(t,x)=f(t,x,u(t,x))+ g\left( t,x ...
S Djebali, Djebali Smail
exaly +3 more sources

Existence of fixed points and measures of weak noncompactness

Nonlinear Analysis: Theory, Methods & Applications, 2009
The author proves the existence of fixed points of an operator $A$ which is defined on a closed convex subset $M$ of a Banach space $X$ into itself and satisfies the following properties: (a) the measure of weak noncompactness of $A(C)$ where $C\subset M$ is not relatively weakly compact is strictly less than the measure of weak compactness ...
Jesus Garcia-Falset
exaly +2 more sources

fixed-point theorems
mathematics
fixed point

fixed point theorems
fixed point theorem
nonlinear integral equations

functional integral equation
interpolation between normed linear spaces
compactness in banach or normed spaces