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Common fixed points of two maps in cone metric spaces

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Abstract

We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.

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References

  1. Abbas, M., Jungck, G.: Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416–420

    Article  MATH  MathSciNet  Google Scholar 

  2. Hardy, G.E., Roggers, T.D.: A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16(2) (1973), 201–206

    MATH  MathSciNet  Google Scholar 

  3. 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 

  4. Ilic, D., Rakocevic, V.: Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), 876–882

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Jungck, G.: Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc., 103 (1988), 977–983

    Article  MATH  MathSciNet  Google Scholar 

  7. Jungck, G., Rhoades, B.E.: Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29(3) (1998), 227–238

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  9. Rezapour, S., Hamlbarani, R.: Some notes on paper “Cone metric spaces and fixed point theorems of contractive mappings.”, J. Math. Anal. Appl., 345 (2008), 719–724

    Article  MATH  MathSciNet  Google Scholar 

  10. Reich, S.: Some remarks concerning contraction mappings, Canad. Math. Bull., 14(2) (1971), 121–124

    MATH  MathSciNet  Google Scholar 

  11. Rhoads, B.E.: A comparison of various definitions of contractive mappings, Trans. Aner. Math. Soc., 26 (1977), 257–290

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

  13. 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. Department of Mathematics, Faculty of Basic and Applied Sciences, International Islamic University, H-10, Islamabad, Pakistan

    Akbar Azam & Muhammad Arshad

  2. Department of Mathematics, F.G. Postgraduate College, H-8, Islamabad, Pakistan

    Akbar Azam

  3. Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan

    Ismat Beg

Authors
  1. Akbar Azam
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  2. Muhammad Arshad
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  3. Ismat Beg
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Correspondence to Ismat Beg.

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Azam, A., Arshad, M. & Beg, I. Common fixed points of two maps in cone metric spaces. Rend. Circ. Mat. Palermo 57, 433–441 (2008). https://doi.org/10.1007/s12215-008-0032-5

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  • DOI: https://doi.org/10.1007/s12215-008-0032-5

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