Fixed point theorems in ordered abstract spaces

Fixed point theorems in ordered abstract spaces
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 135 (2007), 2505-2517

DOI: https://doi.org/10.1090/S0002-9939-07-08729-1

Published electronically: March 21, 2007

PDF | Request permission

We extend some fixed point theorems in $L$-spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.

References

André C. M. Ran and Martine C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435–1443. MR 2053350, DOI 10.1090/S0002-9939-03-07220-4
Juan J. Nieto and Rosana Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), no. 3, 223–239 (2006). MR 2212687, DOI 10.1007/s11083-005-9018-5
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.
Adrian Petruşel and Ioan A. Rus, Fixed point theorems in ordered $L$-spaces, Proc. Amer. Math. Soc. 134 (2006), no. 2, 411–418. MR 2176009, DOI 10.1090/S0002-9939-05-07982-7
M. Fréchet, Les espaces abstraits, Gauthiers-Villars, Paris, 1928.
Phil Diamond and Peter Kloeden, Metric spaces of fuzzy sets, World Scientific Publishing Co., Inc., River Edge, NJ, 1994. Theory and applications. MR 1337027, DOI 10.1142/2326
Seppo Heikkilä and V. Lakshmikantham, Monotone iterative techniques for discontinuous nonlinear differential equations, Monographs and Textbooks in Pure and Applied Mathematics, vol. 181, Marcel Dekker, Inc., New York, 1994. MR 1280028