Results 21 to 30 of about 855 (128)
Weak solutions for the dynamic equations $x^{\Delta(m)}(t) = f (t; x(t))$ on time scales [PDF]
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
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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.
Józef Bana ́, Kishin Sadarangani
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Filomat, 2023 In the present paper we introduce a new concept of measuring, called the measure of non-almost weak noncompactness. We use this measure to characterize the almost weakly compact operators and to investigate the generalized Schechter essential spectrum of the sum of two bounded linear operators.
Rabeb Aydi, Bilel Krichen
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Relative $$\varepsilon$$-pseudo weak demicompactness and measures of weak noncompactness
Annals of Functional Analysis, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ines Chtourou, Bilel Krichen
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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.
Mieczysław Cichoń
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Solvability of a general nonlinear integral equation in $L^1$ spaces by means of a measure of weak noncompactness [PDF]
Journal of Integral Equations and Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fuli Wang
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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.
B. Cascales, Antonio Pérez, M. Raja
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On Darbo-Sadovskii's fixed point theorems type for abstract measures of (weak) noncompactness [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jesús Garcı́a-Falset, Khalid Latrach
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Measures of weak noncompactness in Banach spaces
Topology and its Applications, 2008 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^*}
C. Angosto, B. Cascales
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Measures of weak noncompactness and nonlinear integral equations of convolution type
Journal of Mathematical Analysis and Applications, 1990 The authors prove that the equation \(x(t)=f[t,\int^{\infty}_{0}k(t- s)x(\phi (s))ds]\) has a monotone solution \(x\in L^ 1(0,\infty)\) if suitable conditions are imposed on the functions f, k, and \(\phi\). The proof builds on measures of weak noncompactness [\textit{F. S. De Blasi}, Bull. Math. Soc. Sci. Math. R. S. R. n. Ser.
Józef Banaś, Zygmunt Knap
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