Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder function spaces
Open Mathematics, 2012 Abstract We show that the generator of any uniformly bounded set-valued Nemytskij composition operator acting between generalized Hölder function metric spaces, with nonempty, bounded, closed, and convex values, is an affine function.
Matkowski Janusz, Wróbel Małgorzata
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ON THE SEQUENTIAL STRONG-WEAK CLOSEDNESS OF THE NEMYTSKIJ MULTIVALUED OPERATOR
Demonstratio Mathematica, 2002 The author gives sufficient conditions for the sequential strong-weak closedness of the Nemytskij operator generated by a measurable multivalued map \(f: \Omega\times E\to 2^F\), with \(\Omega\) being a measure space and \(E\), \(F\) being separable Banach spaces.
Hong Thai Nguyen
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On uniformly continuous Nemytskij operators generated by set-valued functions [PDF]
Aequationes Mathematicae, 2010 The properties of superposition operators generated by set-valued functions are studied. The main result is the following. Theorem. Let \(I = [0, 1]\) and \(Y\) be a real normed linear space, \(Z\) be a Banach space and let \(C\) be a convex cone in \(Y\). Assume that \(\gamma: [0, \infty) \rightarrow [0, \infty)\) is continuous at \(0\), \(\gamma(0) =
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Journal of Mathematical Analysis and Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Małgorzata Wröbel
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ON NEMYTSKIJ OPERATOR OF SUBSTITUTION IN THE C1 SPACE OF SET-VALUED FUNCTIONS
Demonstratio Mathematica, 2008 AbstractWe consider the Nemytskij operator, i.e., the operator of substitution, defined by (
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Continuity and Fr�chet-differentiability of Nemytskij operators in H�lder spaces
Monatshefte Fur Mathematik, 1992 The paper is a continuation of \textit{M. Goebel} [Glasg. Math. J. 33, No. 1, 1-5 (1991; Zbl 0724.47041)] and deals with Nemytskij operators (superposition operators), \((Fy)(t)=f(t,y(t))\), which are generated by a function \(f: [a,b]\times\mathbb{R}^ n\to\mathbb{R}\).
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Uniformly bounded Nemytskij operators acting between the Banach spaces of generalized Hölder functions [PDF]
Journal of Applied Mathematics and Computational Mechanics, 2017 Małgorzata Wröbel
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On Fréchet-differentiability of Nemytskij operators acting in Hölder spaces [PDF]
Glasgow Mathematical Journal, 1991 In any field of nonlinear analysis Nemytskij operators, the superposition operators generated by appropriate functions, play a crucial part. Their analytic properties depend on the postulated properties of the defining function and on the function space in which they are considered. A rich source for related questions is the monograph by J.
Mehmeti Feli Ali, Serge Nicaise
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Uniformly continuous set-valued composition operators in the space of total φ-bidimensional variation in the sense of Riesz [PDF]
Opuscula Mathematica, 2010 In this paper we prove that if a Nemytskij composition operator, generated by a function of three variables in which the third variable is a function one, maps a suitable large subset of the space of functions of bounded total \(\varphi\)-bidimensional ...
Wadie Aziz +3 more
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On the Autonomous Nemytskij Operator in Hölder Spaces
Zeitschrift für Analysis und ihre Anwendungen, 1999 The paper is devoted to the autonomous Nemytskij operator (superposition operator) in Hölder spaces H^{k+\alpha}[a,b], (k, \alpha) \in \mathbb Z_+ \times [0, 1]. We study acting, continuity, Lipschitz continuity, and Fréchet differentiability conditions. For
Goebel, M., Sachweh, F.
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