International Journal of Nonlinear Analysis and Applications
Fixed point theorems for single valued mappings satisfying the ordered nonexpansive conditions on ultrametric and non-Archimedean normed spaces
Document Type : Research Paper
Authors
K. N. Toosi University of Technology
Abstract
In this paper, some fixed point theorems for non-expansive mappings in partially ordered spherically complete ultrametric spaces are proved. In addition, we investigate the existence of fixed points for nonexpansive mappings in partially ordered non-Archimedean normed spaces. Finally, we give some examples to discuss the assumptions and support of these theorems.
Keywords
[1] R. P. Agarwal, M. A. El-Gebeily and D. O’Regan, Generalized contractions in partially ordered metric spaces,Appl. Anal. 87(1) (2008), 109–116.
[2] L. Gaji´c, On ultrametric space, Novi Sad J. Math. 31(2) (2001), 69–71.
[3] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics,28. Cambridge University Press, Cambridge, 1990.
[4] W. A. Kirk and N. Shahzad, Some fixed point results in ultrametric spaces, Topology Appl. 159(15) (2012),3327–3334.
[5] J. J. Nieto, R. L. Pouso and R. Rodr´ıguez-L´opez, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc. 135(8) (2007), 2505–2517.
[6] J. J. Nieto and R. Rodriıguez-Lopez. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239.
[7] D. O’Regan and A. Petru¸sel, Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl., 341(2) (2008), 1241–1252.
[8] C. Petalas and T. Vidalis, A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc. 118(3) (1993), 819–821.
[9] A. Petru¸sel and I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134(2) (2006),411–418
[10] S. Priess-Crampe and P. Ribenboim, Fixed point and attractor theorems for ultrametric spaces, Forum Math. 12(1) (2000), 53–64.
[11] 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.
[12] A. C. M. Van Rooij, Non-Archimedean functional analysis, Marcel Dekker, Newyork, 1978.
[2] L. Gaji´c, On ultrametric space, Novi Sad J. Math. 31(2) (2001), 69–71.
[3] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics,28. Cambridge University Press, Cambridge, 1990.
[4] W. A. Kirk and N. Shahzad, Some fixed point results in ultrametric spaces, Topology Appl. 159(15) (2012),3327–3334.
[5] J. J. Nieto, R. L. Pouso and R. Rodr´ıguez-L´opez, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc. 135(8) (2007), 2505–2517.
[6] J. J. Nieto and R. Rodriıguez-Lopez. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239.
[7] D. O’Regan and A. Petru¸sel, Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl., 341(2) (2008), 1241–1252.
[8] C. Petalas and T. Vidalis, A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc. 118(3) (1993), 819–821.
[9] A. Petru¸sel and I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134(2) (2006),411–418
[10] S. Priess-Crampe and P. Ribenboim, Fixed point and attractor theorems for ultrametric spaces, Forum Math. 12(1) (2000), 53–64.
[11] 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.
[12] A. C. M. Van Rooij, Non-Archimedean functional analysis, Marcel Dekker, Newyork, 1978.
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Volume 12, Issue 1
May 2021Pages 735-740
- Receive Date: 07 January 2015
- Revise Date: 13 December 2019
- Accept Date: 09 March 2020
- First Publish Date: 13 March 2021