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Fixed point theorems in ordered abstract spaces
Author(s):
Juan
J.
Nieto;
Rodrigo
L.
Pouso;
Rosana
Rodríguez-López
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2505-2517.
MSC (2000):
Primary 47H10
Posted:
March 21, 2007
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Abstract:
We extend some fixed point theorems in  -spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.
References:
-
- 1.
- A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443. MR 2053350 (2005a:47112)
- 2.
- J.J. Nieto, R. Rodríguez-López, Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations, Order, 22 (2005), 223-239. MR 2212687
- 3.
- J.J. Nieto, R. Rodríguez-López, Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations, Acta Math. Sinica (English Series), to appear.
- 4.
- A. Petrusel, I.A. Rus, Fixed point theorems in ordered
 -spaces, Proc. Amer. Math. Soc. 134 (2006), 411-418. MR 2176009 (2006g:47097) - 5.
- M. Fréchet, Les espaces abstraits, Gauthiers-Villars, Paris, 1928.
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Additional Information:
Juan
J.
Nieto
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, {\rm 15782}, Spain
Email:
amnieto@usc.es
Rodrigo
L.
Pouso
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, {\rm 15782}, Spain
Email:
rodrigolp@usc.es
Rosana
Rodríguez-López
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, {\rm 15782}, Spain
Email:
amrosana@usc.es
DOI:
10.1090/S0002-9939-07-08729-1
PII:
S 0002-9939(07)08729-1
Keywords:
Fixed point,
partially ordered set,
$L$-spaces.
Received by editor(s):
October 20, 2005
Received by editor(s) in revised form:
March 20, 2006
Posted:
March 21, 2007
Additional Notes:
This research was partially supported by Ministerio de Educación y Ciencia and FEDER, project MTM2004--06652--C03--01, and by Xunta de Galicia and FEDER, project PGIDIT05PXIC20702PN
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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