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Functional Analysis and Its Applications

, Volume 46, Issue 1, pp 62–65 | Cite as

Quasi-contractions on a nonnormal cone metric space

  • Ljiljana Gajić
  • Vladimir Rakočević
Brief Communications

Abstract

Ilić and Rakočević [6] proved a fixed point theorem for quasi-contractive mappings on cone metric spaces when the underlying cone is normal. Recently, Z. Kadelburg, S. Radenović, and V. Rakočević obtained a similar result without using the normality condition but only for a contractive constant λ ∈ (0, 1/2) [8]. In this note, using a new method of proof, we prove this theorem for any contractive constant λ ∈ (0, 1).

Key words

Fixed point cone metric space quasi-contraction 

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References

  1. [1]
    M. Abbas and B. E. Rhoades, Appl. Math. Lett., 22:4 (2009), 511–515.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    C. D. Bari and P. Vetro, Rend. Circ. Mat. Palermo, 57:2 (2008), 279–285.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Lj. B. Ćirić, Proc. Amer. Math. Sc., 45 (1974), 267–273.MATHGoogle Scholar
  4. [4]
    K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.MATHGoogle Scholar
  5. [5]
    L.-G. Huang and X. Zhang, J. Math. Anal. Appl., 332:2 (2007), 1468–1476.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    D. Ilić and V. Rakočević, Appl. Math. Lett., 22:5 (2009), 728–731.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    G. Jungck, S. Radenović, S. Radojević, and V. Rakočević, Fixed Point Theory and Applications, 2009, Art. ID 643640, doi: 10.1155/2009/643640.Google Scholar
  8. [8]
    Z. Kadelburg, S. Radenović, and V. Rakočević, Appl. Math. Lett., 22:11 (2009), 1674–1679.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of Mathematics, Faculty of ScienceUniversity of Novi SadNovi SadSerbia
  2. 2.Faculty of Sciences and Mathematics Department of MathematicsUniversity of NišNišSerbia

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