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ϕ-pairs and common fixed points in cone metric spaces

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Abstract

In this paper we introduce a contractive condition, called ϕ-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 ϕ-pairs. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.

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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

    Article  MATH  MathSciNet  Google Scholar 

  2. Huang, L.-G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476

    Article  MATH  MathSciNet  Google Scholar 

  3. Jungck, G.: Commuting maps and fixed points, Amer. Math. Monthly, 83 (1976), 261–263

    Article  MATH  MathSciNet  Google Scholar 

  4. Jungck, G.: Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771–779

    Article  MATH  MathSciNet  Google Scholar 

  5. Jungck, G.: Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. (FJMS), 4 (1996), 199–215

    MATH  MathSciNet  Google Scholar 

  6. Jungck, G., Rhoades, B.E: Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227–238

    MATH  MathSciNet  Google Scholar 

  7. Pant, R.P.: Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188 (1994), 436–440

    Article  MATH  MathSciNet  Google Scholar 

  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

    Article  MATH  MathSciNet  Google Scholar 

  9. Sessa, S.: On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. Soc., 32 (1982), 149–153

    MathSciNet  Google Scholar 

  10. Vetro, P.: Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 56 (2007), 464–468

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, Università degli Studi di Palermo, Via Archirafi, 34 - 90123, Palermo, Italy

    Cristina Di Bari & Pasquale Vetro

Authors
  1. Cristina Di Bari
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  2. Pasquale Vetro
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Corresponding author

Correspondence to Cristina Di Bari.

Additional information

The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.

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Di Bari, C., Vetro, P. ϕ-pairs and common fixed points in cone metric spaces. Rend. Circ. Mat. Palermo 57, 279–285 (2008). https://doi.org/10.1007/s12215-008-0020-9

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  • DOI: https://doi.org/10.1007/s12215-008-0020-9

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