Weak solutions of a boundary value problem for nonlinear ordinary differential equation of second order in Banach spaces
Danuta Ozdarska, Stanisław Szufla (1993)
Mathematica Slovaca
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Danuta Ozdarska, Stanisław Szufla (1993)
Mathematica Slovaca
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I. Kubiaczyk, S. Szufla (1982)
Publications de l'Institut Mathématique
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Dariusz Bugajewski (1994)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we investigate weakly continuous solutions of some integral equations in Banach spaces. Moreover, we prove a fixed point theorem which is very useful in our considerations.
Jozef Banas, Antonio Martinón (1990)
Extracta Mathematicae
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The notion of a measure of noncompactness turns out to be a very important and useful tool in many branches of mathematical analysis. The current state of this theory and its applications are presented in the books [1,4,11] for example. The notion of a measure of weak noncompactness was introduced by De Blasi [8] and was subsequently used in numerous branches of functional analysis and the theory of differential and integral equations (cf. [2,3,9,10,11], for instance). ...
Banas, Jozef, Martinón, Antonio (1995)
Portugaliae Mathematica
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Ali Ülger (2001)
Colloquium Mathematicae
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Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
Ireneusz Kubiaczyk (1984)
Annales Polonici Mathematici
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Mieczysław Cichoń, Ireneusz Kubiaczyk (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we prove an existence theorem for the Hammerstein integral equation , where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.