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1
Content available remote Superposition Operators in the Space of Functions of Waterman-Shiba Bounded Variation
100%
Giménez J. , Merentes N. , Rodriguez L.
Commentationes Mathematicae
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2014
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tom Vol 54, No. 1
79--93
EN
In this paper we present a necessary condition for an autonomous superposition operator to act in the space of functions of Waterman-Shiba bounded variation. We also show that if a (general) superposition operator applies such space into itself and it is uniformly bounded, then its generating function satisfies a weak Matkowski condition.
2
Content available On some properties of the superposition operator on topological manifolds
100%
Dronka J.
Opuscula Mathematica
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2010
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tom Vol. 30, no. 1
69-77
EN
In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
3
Content available remote The solvability of functional quadratic volterra-urysohn integral equations on the half line
100%
Metwali M. M. A.
Fasciculi Mathematici
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2018
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tom Nr 61
109--123
EN
We study the solvability of general quadratic Volterra integral equations in the space of Lebesgue integrable functions on the half line. Using the conjunction of the technique of measures of weak noncompactness with modified Schauder fixed point principle we show that the integral equation, under certain conditions, has at least one solution. Moreover, that result generalizes several ones obtained earlier in many research papers and monographs.
4
Content available Monotonic solutions for quadratic integral equations
88%
Cichoń M. , Metwali M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
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nr 2
157-171
EN
Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
5
Content available remote Uniformly continuous superposition operators in the space of functions of bounded n-dimensional Φ-variation
75%
Bracamonte M. , Ereú J. , Giménez J. , Merentes N.
Demonstratio Mathematica
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2014
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tom Vol. 47, nr 1
56--68
EN
We prove that if a superposition operator maps a subset of the space of all metric-vector-space-valued-functions of bounded n-dimensional Φ-variation into another such space, and is uniformly continuous, then the generating function of the operator is an affine function in the functional variable.
6
Content available remote Superposition operators on sequence spaces defined by (phi)-functions
63%
Kolk E.
Demonstratio Mathematica
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2004
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tom Vol. 37, nr 1
159--175
7
Content available Multi-valued superpositions
54%
Appell J. , Thái N. H. , De Pascale E. , Zabreĭko P. P.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction.......................................................................................................... 5 1. Multifunctions and selections............................................................................... 7  1. Multifunctions and selections.................................................................. 7  2. Continuous multifunctions and selections........................................... 9  3. Measurable multifunctions and selections............................................ 16 2. Multifunctions of two variables............................................................................... 19  4. Carathéodory multifunctions and selections......................................... 19  5. The Scorza Dragoni property..................................................................... 25  6. Implicit function theorems......................................................................... 32 3. The superposition operator................................................................................... 33  7. The superposition operator in the space S........................................... 34  8. The superposition operator in ideal spaces......................................... 39  9. The superposition operator in the space C........................................... 47 4. Closures and convexifications.............................................................................. 49  10. Strong closures........................................................................................ 49  11. Convexifications....................................................................................... 52  12. Weak closures.......................................................................................... 56 5. Fixed points and integral inclusions..................................................................... 59  13. Fixed point theorems for multi-valued operators................................ 60  14. Hammerstein integral inclusions........................................................ 63  15. A reduction method................................................................................... 68 6. Applications............................................................................................................... 72  16. Applications to elliptic systems.............................................................. 72  17. Applications to nonlinear oscillations................................................. 75  18. Applications to relay problems.............................................................. 78 References.................................................................................................................... 81 Index of symbols........................................................................................................... 93 Index of terms................................................................................................................ 95
8
Content available remote On some approximation problems in Musielak-Orlicz spaces of multifunctions
51%
Kasperski A.
Demonstratio Mathematica
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2004
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tom Vol. 37, nr 2
393--406
EN
We introduce the Musielak-Orlicz spaces of multifunctions Xmphi and Xc,m,phi. We prove that these spaces are complete. Also, we get some convergence and approximation theorems in these spaces.
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