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Multifunctions of two variables: examples and counterexamples

100%
Appell J.
Banach Center Publications
|
1996
|
tom 35
|
nr 1
119-128
EN
A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.
2
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The importance of being Orlicz

100%
Appell J.
Banach Center Publications
|
2004
|
tom 64
|
nr 1
21-28
3
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Multi-valued superpositions

56%
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
4
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Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator

51%
B. Antonevich A., Appell J., Zabreĭko P. P.
Studia Mathematica
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1994-1995
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tom 112
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nr 1
1-11
EN
We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.
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