Fixed points of order preserving contractions
Keywords:
Contraction, Order preserving map, Fixed point propertyAbstract
In this paper, we analyze fixed points of order preserving contractions on ordered metric spaces. Fixed point property of such maps is characterized for bounded convex subsets of the Euclidean plane.
References
[1] R.P. Agarwal, B. Xu, W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 288 (2003) 852–869.
[2] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications, Fund. Math. 3 (1992), 133-181. http: //eudml.org/doc/213289
[3] T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393. DOI:10.1016/j.na.2005.10.017
[4] L. E. J. Brouwer, Uber Abbildung von Mannigfaltigkeiten, Mathematische Annalen ¨ 38(71) (1912), 97-115. doi.org/10. 1007/BF01456931
[5] E. T. Copson, Metric Spaces, Cambridge University Press, 1968. https://doi.org/10.1002/zamm.19690490919
[6] S. George and D. Wulbert, Subsets of the square with the continuous and order preserving fixed point propert, Nonliner Analysis 75 (2012), 2581-2590. DOI:10.1016/j.na.2011.11.004
[7] G. Markowsky, Chain-complete posets and directed sets with applications, Algebra Universalis 6 (1976), 53-68. DOI: 10.1007/BF02485815
[8] J. J. Nieto and R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239. DOI:10.1007/s11083-005-9018-5
[9] A. C. M. Ran and 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.DOI:10.2307/4097222
[10] J. Schauder, Der Fixpunktsatz in Funktionalr¨aumen, Studia Math. 2 (1930), 171-180. http://eudml.org/doc/217247
[11] A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285-309. https://doi. org/10.2140/pjm.1955.5.285
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