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A fixed point theorem and its application to integral equations in modular function spaces
Author(s):
A.
Ait
Taleb;
E.
Hanebaly
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2335-2342.
MSC (1991):
Primary 46A80, 47H10, 45G10, 46E30
Posted:
April 9, 1999
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Abstract:
In this paper we present a fixed point theorem of Banach type in modular space. We give an application of this result to a nonlinear integral equation in Musielak-Orlicz space.
References:
- [1]
- A. Ait Taleb, Points fixes et Applications aux equations integrales dans les espaces modulaires. These de 3eme cycle, Departement de Mathematiques et Informatique, Rabat (1996).
- [2]
- K. Deimling, Nonlinear Functional Analysis, Springer Verlag, (1985). MR 86j:47001
- [3]
- K. Goebel-S. Reich, Uniform convexity, Hyperbolic Geometry and nonexpansive mappings, Dekker, (1984). MR 86d:58012
- [4]
- K. Goebel-W.A. Kirk, Topics in metric fixed point theory, Cambrige University Press, Cambridge (1990). MR 92c:47070
- [5]
- M.A. Khamsi-W.M. Kozlowski-S. Reich, Fixed point theory in modular Function spaces. Nonlinear Analysis, theory, methods and Applications. vol.14.
 11 (1990). 935-953. MR 91d:47042 - [6]
- M.A. Khamsi, Nonlinear semigroups in modular Function space thèse d' état. Departement de Mathematiques, Rabat (1994). MR 93g:47085
- [7]
- W.M. Kozlowski, Modular function spaces. Dekker (1988). CMP 98:02
- [8]
- J. Musielak, Orlicz spaces and modular spaces, Lecture notes in Mathematics, vol 1034, Springer Verlag (1983). MR 85m:46028
- [9]
- E. Zeidler, Nonlinear Functional Analysis and its Applications tome III, Springer Verlag (1985). MR 90b:49005
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Additional Information:
A.
Ait
Taleb
Affiliation:
Department of Mathematics and Informatic, Faculte des Sciences, Universite Mohammed V, BP. 1014, Rabat, Morocco
E.
Hanebaly
Affiliation:
Department of Mathematics and Informatic, Faculte des Sciences, Universite Mohammed V, BP. 1014, Rabat, Morocco
DOI:
10.1090/S0002-9939-99-04779-6
PII:
S 0002-9939(99)04779-6
Keywords:
Modular space,
fixed point,
integral equation
Received by editor(s):
January 5, 1996
Received by editor(s) in revised form:
October 30, 1997
Posted:
April 9, 1999
Communicated by:
Dale Alspach
Copyright of article:
Copyright
1999,
American Mathematical Society
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