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An order on subsets of cone metric spaces and fixed points of set-valued contractions. (English) Zbl 1187.47041

Summary: We introduce a new order on the subsets of cone metric spaces and, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:

[1] Huang L-G, Zhang X: Cone metric spaces and fixed point theorems of contractive mappings.Journal of Mathematical Analysis and Applications 2007,332(2):1468-1476. 10.1016/j.jmaa.2005.03.087 · Zbl 1118.54022
[2] Abbas M, Rhoades BE: Fixed and periodic point results in cone metric spaces.Applied Mathematics Letters 2009,22(4):511-515. 10.1016/j.aml.2008.07.001 · Zbl 1167.54014
[3] Arshad, M.; Azam, A.; Vetro, P., Some common fixed point results in cone metric spaces, 11 (2009) · Zbl 1167.54313
[4] Ilic D, Rakocevic V: Common fixed points for maps on cone metric space.Journal of Mathematical Analysis and Applications 2008,341(2):876-882. 10.1016/j.jmaa.2007.10.065 · Zbl 1156.54023
[5] Ilic D, Rakocevic V: Quasi-contraction on a cone metric space.Applied Mathematics Letters 2009,22(5):728-731. 10.1016/j.aml.2008.08.011 · Zbl 1179.54060
[6] Jankovic, S.; Kadelburg, Z.; Radenovic, S.; Rhoades, BE, Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces, 16 (2009) · Zbl 1186.54035
[7] Jungck, G.; Radenovic, S.; Radojevic, S.; Rakocevic, V., Common fixed point theorems for weakly compatible pairs on cone metric spaces, 13 (2009) · Zbl 1190.54032
[8] Raja, P.; Vaezpour, SM, Some extensions of Banach’s contraction principle in complete cone metric spaces, 11 (2008) · Zbl 1148.54339
[9] Wardowski D: Endpoints and fixed points of set-valued contractions in cone metric spaces.Nonlinear Analysis: Theory, Methods & Applications 2009,71(1-2):512-516. 10.1016/j.na.2008.10.089 · Zbl 1169.54023
[10] Deimling K: Nonlinear Functional Analysis. Springer, Berlin, Germany; 1985:xiv+450. · Zbl 1257.47059
[11] Denkowski Z, Migórski S, Papageorgiou NS: An Introduction to Nonlinear Analysis: Applications. Kluwer Academic Publishers, Boston, Mass, USA; 2003:xii+823. · Zbl 1054.47001
[12] Rezapour Sh, Hamlbarani R: Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”.Journal of Mathematical Analysis and Applications 2008,345(2):719-724. 10.1016/j.jmaa.2008.04.049 · Zbl 1145.54045
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