Results 11 to 20 of about 89 (78)

Remarks on a measure of weak noncompactness in the Lebesgue space [PDF]

Bulletin of the Australian Mathematical Society, 1995
Using the concept of equi-integrability we introduce a measure of weak noncompactness in the Lebesgue space L1(0, l). We show that this measure is equal to the classical De Blasi measure of weak noncompactness.
Banaś, Józef, Sadarangani, Kishin
openaire   +3 more sources

Measure of weak noncompactness and real interpolation of operators [PDF]

Bulletin of the Australian Mathematical Society, 2000
A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of the operators T: Ai → Bi, i = 0, 1 is weakly compact, then so is T : Aθ,p → Bθ,
Andrzej Krzysztof Kryczka, Stanisław Prus, Mariusz Szczepanik   +2 more
openaire   +1 more source

Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces

Electronic Journal of Qualitative Theory of Differential Equations, 2010
The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions.
Mouffak Benchohra, John Graef, F. Mostefai   +2 more
doaj   +1 more source

Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications [PDF]

Axioms, 2019
In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra.
Mohamed Amine Farid, Karim Chaira, El Miloudi Marhrani, Mohamed Aamri   +3 more
openaire   +2 more sources

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Boundary Value Problems, 2018
The aim of this paper is to investigate the existence of weak solutions for a boundary value problem of a second order differential equation. As the main tool, we apply a Krasnosel’skii type fixed point theorem in conjunction with the technique of ...
Shiyou Weng, Fuli Wang
doaj   +1 more source

Radon–Nikodým indexes and measures of weak noncompactness

Journal of Functional Analysis, 2014
The authors introduce and study certain indices related to the Radon-Nikodým property in Banach spaces. Interesting quantitative versions of classic results in RNP are proved. Let \(E\) be a Banach space and \((\Omega,\Sigma,\mu)\) a complete probability space.
Cascales, B., Pérez, A., Raja, M.
openaire   +3 more sources

Weak Solutions for Nonlinear Fractional Differential Equations in Banach Spaces

Discrete Dynamics in Nature and Society, 2012
We discuss the existence of weak solutions for a nonlinear boundary value problem of fractional differential equations in Banach space. Our analysis relies on the Mönch's fixed point theorem combined with the technique of measures of weak noncompactness.
Wen-Xue Zhou, Ying-Xiang Chang, Hai-Zhong Liu   +2 more
doaj   +1 more source

Existence and quantum calculus of weak solutions for a class of two-dimensional Schrödinger equations in C+ $\mathbb{C}_{+}$

Boundary Value Problems, 2018
The aim of this paper is to investigate the existence of weak solutions for a two-dimensional Schrödinger equation with a singular potential in C+ $\mathbb{C}_{+}$.
Yifan Xing, Jinhui Zhao
doaj   +1 more source

Measures of weak noncompactness in Banach spaces

Topology and its Applications, 2009
For a bounded subset \(H\) of a Banach space \(E\), the following quantities are considered: \[ \omega(H) = \inf\{\varepsilon > 0: H \subset K_\varepsilon + \varepsilon B_E \text{ and } K_\varepsilon \subset E \text{ is } w-\text{compact}\}; \] \[ \gamma(H) = \sup\left\{\left|\lim_n \lim_m f_m(x_n) - \lim_m \lim_n f_m(x_n) \right|: (f_m) \subset B_{E^*}
Angosto, C., Cascales, B.
openaire   +2 more sources

Weak solutions for the dynamic equations $x^{\Delta(m)}(t) = f (t; x(t))$ on time scales

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this paper we prove the existence of weak solutions of the dynamic Cauchy problem \begin{equation*} \begin{split} x^{(\Delta m)}(t)&=f(t,x(t)),\quad t\in T, \\ x(0)&=0, \\ x^\Delta (0)&=\eta _1 ,\dots,x^{(\Delta (m-1))}(0)=\eta _{m-1},\quad \eta ...
Aneta Sikorska-Nowak, Samir Saker
doaj   +1 more source