Results 61 to 70 of about 70 (70)

Weakly demicompact linear operators and axiomatic measures of weak noncompactness

Mathematica Slovaca, 2019
Abstract In this paper, we study the relationship between the class of weakly demicompact linear operators, introduced in [KRICHEN, B.—O’REGAN, D.: On the class of relatively weakly demicompact nonlinear operators, Fixed Point Theory 19 (2018), 625–630], and measures of weak noncompactness of linear operators with respect to an axiomatic one. Moreover,
Bilel Krichen, Donal O’Regan
openaire   +1 more source

On measures of weak noncompactness

Publicationes Mathematicae Debrecen, 1994
A notion of measure of weak noncompactness is introduced which generalizes the De Blasi measure of weak noncompactness. Some properties of this generalized measure are proved. The existence of bounded weak solutions of certain differential equations is shown.
openaire   +1 more source

Convexification of super weakly compact sets and measure of super weak noncompactness

Proceedings of the American Mathematical Society, 2021
Let \(A\) be a subset of a Banach space \(X\), and let \(\textrm{co}(A)\) and \(\textrm{aff}(A)\) denote the convex hull and the affine hull of \(A\). We say that a subset \(B\) of a Banach space \(Y\) is \textit{finitely representable in \(A\)} if for every finite subset \(B_0\) of \(B\) and \(r>1\) there is a finite subset \(A_0\) of \(A\) and an ...
openaire   +2 more sources

Measures of Weak Noncompactness and Fixed Points

2017
The interaction between measures of weak noncompactness and fixed point theory is really strong and fruitful. In particular, measures of weak noncompactness play a significant role in topological fixed point problems. The purpose of this chapter is to exhibit the importance of the use of measures of weak noncompactness in topological fixed point theory
Agnieszka Chlebowicz, Mohamed-Aziz Taoudi   +1 more
openaire   +1 more source

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 ...
openaire   +1 more source

Measures of weak noncompactness, nonlinear leray-schauder alternatives in banach algebras satisfying condition (p) and an application

Quaestiones Mathematicae, 2015
In this paper, we establish some new nonlinear Leray-Schauder alternatives for the sum and the product of weakly sequentially continuous operators in Banach algebras satisfying certain sequential condition (P). The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
Ali, Amro Alsheikh, Amar, Afif Ben
openaire   +2 more sources

Measure of weak noncompactness, some new properties in Fredholm theory, characterization of the Schechter essential spectrum and application to transport operators

Ricerche di Matematica, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdelmoumen, Boulbeba, Jeribi, Aref, Mnif, Maher   +2 more
openaire   +2 more sources

Measures of weak noncompactness and fixed point theory in banach algebras satisfying condition (P)

2017
The aim of this paper is to prove some new fixed point theorems in a nonempty closed convex subset of a Banach algebra satisfying a sequential condition (P) in a weak topology setting.
Ben Amar, Afif, O’Regan, Donal
openaire   +1 more source

Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the lebesgue space

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author shows that, for a subset \(X\) of \(L_1\) which is compact in measure, the continuity, demicontinuity, and weak sequential continuity of \(T: X\to X\) are equivalent. This makes it possible to enlarge the applicability of fixed point theorems involving weakly condensing operators.
openaire   +2 more sources

Measure of weak noncompactness and fixed point theorems

1981
openaire   +2 more sources