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.
Chaira Karim +2 more
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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.
Bilel Krichen
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Measure of weak noncompactness under complex interpolation [PDF]
Studia Mathematica, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrzej Kryczka, Stanisław Prus
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Real Interpolation and Measure of Weak Noncompactness
Mathematische Nachrichten, 1995 AbstractBehavior of weak measures of noncompactness under real interpolation is investigated. It is shown that “convexity type” theorems hold true for weak measures of noncompactness.
Aksoy, A. G., Maligranda, Lech
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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.
Garcia-Falset, Jesús, Latrach, Khalid
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Multivalued fixed point theorems in terms of weak topology and measure of weak noncompactness
Journal of Mathematical Analysis and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paola Rubbioni, Tiziana Cardinali
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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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APPLICATION OF MEASURES OF WEAK NONCOMPACTNESS TO A NONLOCAL DARBOUX PROBLEM
Demonstratio Mathematica, 2009 AbstractIn this paper we study the existence of pseudosolutions of a nonlocal hyperbolic Darboux problem for the ...
Piotr Majcher, Sushil Sharma
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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^*}
Bernardo 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 Banas
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