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Generalized asymptotic contractions

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Abstract

In recent years, there have been considerable interests in the study of contractions and their generalizations. In this paper, some new concepts of asymptotic contractions of Boyd–Wong type and a generalized Meir–Keeler type are introduced and compared. Furthermore, various fixed point results for such classes of mappings in the context of modular metric spaces are derived. Most of the results are new even for metric spaces.

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References

  1. Abdou, A.A., Khamsi, M.A.: Fixed point results of pointwise contractions in modular metric spaces. Fixed Point Theory Appl. (2013), doi:10.1186/1687-1812-2013-163

  2. Arav, M., Castillo Santos, F.E., Reich, S., Zaslavski, A.J.: A note on asymptotic contractions. Fixed Point Theory Appl. 2007, 039465 (2007), doi:10.1155/2007/39465

  3. Boyd, D.W., Wong, J.S.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  4. Banach, S.: Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fundam. Math. 3, 133–181 (1922)

    Article  MATH  Google Scholar 

  5. Briseid, E.M.: A rate of convergence for asymptotic contractions. J. Math. Anal. Appl. 330, 364–376 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chistyakov, V.V.: Modular metric spaces, I: basic concepts. Nonlinear Anal. 72, 1–14 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jachymski, J., Jozwik, I.: On Kirk’s asymptotic contractions. J. Math. Anal. Appl. 300, 147–159 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Khamsi, M.A.: Generalized metric spaces: a survey. J. Fixed Point Theory Appl. 17, 455–475 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  9. Khamsi, M.A., Kozlowski, W.M.: Fixed Point Theory in Modular Function Spaces. Birkhauser, New York (2015)

    Book  MATH  Google Scholar 

  10. Khamsi, M.A., Kozlowski, W.M., Reich, S.: Fixed point theory in modular function spaces. Nonlinear Anal. 14, 935–953 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kirk, W.A.: Fixed points of asymptotic contractions. J. Math. Anal. Appl. 277, 645–650 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Meir, A., Keeler, E.: A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326–329 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  13. Musielak, J., Orlicz, W.: On modular spaces. Stud. Math. 18, 49–65 (1959)

    Article  MATH  Google Scholar 

  14. Nakano, H.: Modulared Semi-Ordered Linear Spaces. Maruzen, Tokyo (1950)

  15. Reich, S., Zaslavski, A.J.: A convergence theorem for asymptotic contractions. J. Fixed Point Theory Appl. 4, 27–33 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Saeidi, S.: Asymptotic contractions of Browder’s and Edelstein’s type. J. Nonlinear Convex Anal. 15, 1105–1111 (2014)

    MATH  MathSciNet  Google Scholar 

  17. Saeidi, S.: Asymptotic contractions of liminf-type. J. Nonlinear Convex Anal. 17, 1583–1591 (2016)

    MATH  MathSciNet  Google Scholar 

  18. Suzuki, T.: Fixed point theorem for asymptotic contractions of Meir–Keeler type in complete metric spaces. Nonlinear Anal. 64, 971–978 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous reviewer for his helpful and constructive comments that greatly contributed to improving the final version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Kurdistan, Sanandaj, Kurdistan , 416, Iran

    Shahram Saeidi

  2. Department of Mathematics Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Faezeh Golkar

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  1. Shahram Saeidi
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  2. Faezeh Golkar
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Correspondence to Shahram Saeidi.

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Saeidi, S., Golkar, F. Generalized asymptotic contractions. J. Fixed Point Theory Appl. 19, 3163–3176 (2017). https://doi.org/10.1007/s11784-017-0478-1

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  • DOI: https://doi.org/10.1007/s11784-017-0478-1

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