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Some fixed point theorems on ordered cone metric spaces. (English) Zbl 1184.54038
Summary: In the present work, two fixed point theorems for self maps on ordered cone metric spaces are proved motivated by [L. G. Huang and X. Zhang, J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] and [A. C. M. Ran and M. C. B. Reuring, Proc. Am. Math. Soc. 132, No. 5, 1435–1443 (2004; Zbl 1060.47056)]

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
References:
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[2]Abbas, M., Rhoades, B.E.: Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22 (2008), 511–515 · Zbl 1167.54014 · doi:10.1016/j.aml.2008.07.001
[3]Agarwal, R.P., El-Gebeily, M.A., O’Regan, D.: Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109–116 · Zbl 1140.47042 · doi:10.1080/00036810701556151
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[7]Huang, L.G., Zhang, H.: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476 · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
[8]Ilić, D., Rakočević, V.: Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), 876–882 · Zbl 1156.54023 · doi:10.1016/j.jmaa.2007.10.065
[9]Ilić, D., Rakočević, V.: Quasi-conraction on cone metric spaces, Appl. Math. Lett., 22 (2009), 728–731 · Zbl 1179.54060 · doi:10.1016/j.aml.2008.08.011
[10]Jungck, G., Radenović, S., Radojević, S., Rakočević, V.: Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., 2009 (2009), 13 pp., Article ID 643840
[11]Nieto, J.J., Lopez, R.R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order, 22 (2005), 223–239 · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[12]Nieto, J.J., Lopez, R.R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica (English Ser.), 23 (2007), 2205–2212 · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[13]O’Regan, D., Petruşel, A.: Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241–1252 · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
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[15]Ran, A.C.M., Reuring, M.C.B: A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443 · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[16]Rezapour, Sh., Hamlbarani, R.: Some notes on the paper ”Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 345 (2008), 719–724 · Zbl 1145.54045 · doi:10.1016/j.jmaa.2008.04.049
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