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Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions

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Abstract

Let (E, τ) be a topological vector space and P a cone in E. We shall define a topology τ P on E so that (E, τ P ) is a normable topological vector space and P is a normal cone with normal constant M = 1. Then by using the norm, we shall give some results about common fixed points of two multifunctions on cone metric spaces.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Azam, A., Arshad, M., Beg, I.: Common fixed points of two maps in cone metric spaces, Rend. Circ. Mat. Palermo, 57 (2008), 433–441

    Article  MATH  MathSciNet  Google Scholar 

  3. Di Bari, C., Vetro, P.: φ-pairs and common fixed points in conemetric spaces, Rend. Circ. Mat. Palermo, 57 (2008), 279–285

    Article  MATH  MathSciNet  Google Scholar 

  4. Di Bari, C., Vetro, P.: Weakly φ-pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 58 (2009), 125–132

    Article  MATH  MathSciNet  Google Scholar 

  5. 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 

  6. Ilić, D., Rakočević, V.: Common fixed points result for maps on cone metric spaces, J. Math. Anal. Appl., 341 (2008), 867–882

    Google Scholar 

  7. Mohebi, H., Sadeghi, H., Rubinov, A.M.: Best approximation in a class of normed spaces with star-shaped cones, Numer. Funct. Anal. Optim., 27 (2006), no. 3–4, 411–436

    Article  MATH  MathSciNet  Google Scholar 

  8. Mohebi, H.: Downward sets and their best simultaneous approximation properties with applications, Numer. Funct. Anal. Optim., 25 (2004), no. 7–8, 685–705

    MATH  MathSciNet  Google Scholar 

  9. 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 

  10. Rezapour, Sh., Derafshpour, M., Hamlbarani, R.: A review on topological properties of cone metric spaces, Submitted.

  11. Rudin, W.: Functional Analysis. McGraw-Hill, Second edition (1991)

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Wardowski, D.: Endpoints and fixed points of set-valued contractions in cone metric spaces, Nonlinear Anal., 71 (2009), 512–516

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Azarbaidjan University of Tarbiat Moallem, Tabriz, Iran

    Shahram Rezapour

  2. Department of Mathematics, Aazad Islamic University, Science and Research Branch, Tehran, Iran

    Hassan Khandani

  3. Department of Mathematics, Amirkabir University of Technology, Tehran, Iran

    Seyyed M. Vaezpour

Authors
  1. Shahram Rezapour
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  2. Hassan Khandani
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  3. Seyyed M. Vaezpour
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Correspondence to Shahram Rezapour.

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Rezapour, S., Khandani, H. & Vaezpour, S.M. Efficacy of cones on topological vector spaces and application to common fixed points of multifunctions. Rend. Circ. Mat. Palermo 59, 185–197 (2010). https://doi.org/10.1007/s12215-010-0014-2

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  • DOI: https://doi.org/10.1007/s12215-010-0014-2

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