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\(\varphi\)-pairs and common fixed points in cone metric spaces. (English) Zbl 1164.54031

Summary: In this paper, we introduce a contractive condition, called \(\varphi\)-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for \(\varphi\)-pairs. We also obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
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References:

[1] Abbas, M., Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416–420 · Zbl 1147.54022
[2] Huang, L.-G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476 · Zbl 1118.54022
[3] Jungck, G.: Commuting maps and fixed points, Amer. Math. Monthly, 83 (1976), 261–263 · Zbl 0321.54025
[4] Jungck, G.: Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771–779 · Zbl 0613.54029
[5] Jungck, G.: Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. (FJMS), 4 (1996), 199–215 · Zbl 0928.54043
[6] Jungck, G., Rhoades, B.E: Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227–238 · Zbl 0904.54034
[7] Pant, R.P.: Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188 (1994), 436–440 · Zbl 0830.54031
[8] 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
[9] Sessa, S.: On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. Soc., 32 (1982), 149–153 · Zbl 0523.54030
[10] Vetro, P.: Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 56 (2007), 464–468 · Zbl 1196.54086
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