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Revista Colombiana de Matemáticas
versión impresa ISSN 0034-7426
Rev.colomb.mat. v.45 n.2 Bogotá jul./dic. 2011
1Universidad de Los Ándes, Mérida, Venezuela. Email: null
2Universidad Central de Venezuela, Caracas, Venezuela. Email: carlos.finol@ciens.ucv.ve
In [5,p. 30], M. A. Krasnosel'skii and Ya. B. Rutickii proposed a problem, which can be reformulated as follows. Let f be an N-function such that f(ts)≤ f(t)f(s), s,t≥ 1. Is there another N-function F such that F(st)≤ F(t)F(s), s,t>0 and equivalent to f on [1,∞)?. We give a necessary and sufficient condition for a positive and constructive solution.
Key words: Orlicz Functions, N-Functions, Submultiplicative Functions, Matuszewska--Orlicz indices.
2000 Mathematics Subject Classification: 39B62, 26B25, 26A51.
En [5,p. 30], M. A. Krasnosel'skii y Ya. B. Rutickii proponen un problema, el cual puede ser reformulado de la siguiente manera: Sea f una N-función tal que f(ts)≤ f(t)f(s) para todo t,s≥ 1. ¿Existe alguna función F tal que F(st)≤ F(s)F(t), s,t≥ 0, que sea equivalente a f en [1,∞)?. En este articulo, damos una condición necesaria y suficiente para una solución positiva y constructiva.
Palabras clave: Funciones de Orlicz, N-funciones, funciones submultiplicativas, indices de Matuszewska--Orlicz.
Texto completo disponible en PDF
References
[1] J. Alexopoulos, 'De la Vallée Poussin's Theorem and Weakly Compact Sets in Orlicz Spaces', QM 17, (1994), 231-248. [ Links ]
[2] T. Andô, 'On Some Properties of Convex Functions', Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys 8, (1960), 413-418. [ Links ]
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[11] W. Matuszewska and W. Orlicz, 'On Certain Properties of φ-Functions', Bull Acad. Polon. Sci. Sér. Math. Astronom Phys 8, (1960), 439-443. [ Links ]
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv45n2a06,
AUTHOR = {Bárcenas, Diomedes and Finol, Carlos},
TITLE = {{On a Problem of Krasnosel'skii and Rutickii}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2011},
volume = {45},
number = {2},
pages = {179--186}
}