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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.
128
(2000),
419-426.
MSC (1991):
Primary 46A80, 47H10, 45G10, 46E30
Posted:
October 12, 1999
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Abstract:
In this paper we present a fixed point theorem of Banach type in modular spaces. Also, we give some applications of this result to a nonlinear integral equation in Musielak-Orlicz space.
References:
- 1.
- A. Ait Taleb, Points fixes et Applications aux equations intégrales dans les espaces modulaires. Thèse de 3ème cycle, Département de Mathématiques et Informatique, Rabat (1996).
- 2.
- K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985. MR 86j:47001
- 3.
- K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry and nonexpansive mappings, Marcel Dekker, New York, 1984. MR 86d:58012
- 4.
- K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Cambridge, 1990. MR 92c:47070
- 5.
- M. A. Khamsi, W. M. Kozlowski, and S. Reich, Fixed point theory in modular function spaces, Nonlinear Anal. 14 (1990), 935-953. MR 91d:47042
- 6.
- M. A. Khamsi, Nonlinear semigroups in modular function space, thèse d'état. Département de Mathématiques, Rabat (1994).
- 7.
- W. M. Kozlowski, Modular function spaces, Marcel Dekker, 1988. MR 99d:46043
- 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. III, Springer-Verlag, 1985. MR 90b:49005
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Additional Information:
A.
Ait
Taleb
Affiliation:
Department of Mathematics and Informatic, University of Mohammed V, BP 1014, Rabat, Morocco
E.
Hanebaly
Affiliation:
Department of Mathematics and Informatic, University of Mohammed V, BP 1014, Rabat, Morocco
DOI:
10.1090/S0002-9939-99-05546-X
PII:
S 0002-9939(99)05546-X
Keywords:
Modular space,
fixed point,
integral equation
Received by editor(s):
October 30, 1997
Posted:
October 12, 1999
Communicated by:
Dale Alspach
Copyright of article:
Copyright
1999,
American Mathematical Society
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