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Common fixed point theorems for weakly compatible pairs on cone metric spaces. (English) Zbl 1190.54032
The results of this paper are related to those in [M. Abbas and G. Jungck, J. Math. Anal. Appl. 341, No. 1, 416–420 (2008; Zbl 1147.54022)], but the assumption of normality of the cone is omitted. These results also generalize some recent theorems of L.-G. Huang and X. Zhang [ibid. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)], P. Vetro [Rend. Circ. Mat. Palermo (2) 56, No. 3, 464–468 (2007; Zbl 1196.54086)] and Sh. Rezapour and R. Hamlbarani [J. Math. Anal. Appl. 345, No. 2, 719–724 (2008; Zbl 1145.54045)].

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:
[1] Abbas, M; Jungck, G, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications, 341, 416-420, (2008) · Zbl 1147.54022
[2] Huang, L-G; Zhang, X, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332, 1468-1476, (2007) · Zbl 1118.54022
[3] Vetro, P, Common fixed points in cone metric spaces, Rendiconti del Circolo Matematico di Palermo, 56, 464-468, (2007) · Zbl 1196.54086
[4] 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, 345, 719-724, (2008) · Zbl 1145.54045
[5] Aliprantis CD, Tourky R: Cones and Duality, Graduate Studies in Mathematics. Volume 84. American Mathematical Society, Providence, RI, USA; 2007:xiv+279. · Zbl 1127.46002
[6] Mohebi, H, Topical functions and their properties in a class of ordered Banach spaces, No. 99, 343-361, (2005), New York, NY, USA · Zbl 1124.90048
[7] Raja, P; Vaezpour, SM, Some extensions of Banach’s contraction principle in complete cone metric spaces, 11, (2008) · Zbl 1148.54339
[8] Ilic, D; Rakocevic, V, Common fixed points for maps on cone metric space, Journal of Mathematical Analysis and Applications, 341, 876-882, (2008) · Zbl 1156.54023
[9] Ilic, D; Rakocevic, V, Quasi-contraction on a cone metric spacestar, open, Applied Mathematics Letters, 22, 728-731, (2009) · Zbl 1179.54060
[10] Wong Y-C, Ng K-F: Partially Ordered Topological Vector Spaces, Oxford Mathematical Monograph. Clarendon Press, Oxford, UK; 1973:x+217.
[11] Rezapour Sh: A review on topological properties of cone metric spaces.Analysis, Topology and Applications (ATA ’08), May-June 2008, Vrnjacka Banja, Serbia
[12] Rhoades, BE, A comparison of various definitions of contractive mappings, Transactions of the American Mathematical Society, 226, 257-290, (1977) · Zbl 0365.54023
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