Fixed points in modular spaces with new type contractivity

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this present paper, we prove a common _xed point theorem for self maps in modular spaces. Also one corollary, which shows that our main theorem is generalized version of the main theorem of [A. Razani, E. Nabizadeh, M.Beyg Mohamadi and S. Homaei Pour, Abs. Appl. Anal. 2007, Article ID 40575] is given.


  • Keywords


    Fixed point; contraction; modular; modular space.

  • References


    1. H. Nakano, Modulared Semi-Ordered Linear Spaces, Tokyo Math. Book Ser., Vol. 1, Maruzen Co., Tokyo, 1950.
    2. J. Musielak and W. Orlicz, "On Modular Spaces", Studia Math., Vol. 18, (1959), pp.49-56.
    3. S. Koshi, T. Shimogaki, "On F{norms of quasi{modular spaces", J. Fac. Sci. Hokkaido Univ. Ser. I, Vol. 15, No. 3, (1961), pp.202-218.
    4. S. Yamamuro, "On conjugate spaces of Nakano spaces", Trans. Amer. Math. Soc., Vol. 90, (1959), pp.291-311.
    5. M.A. Krasnoselskii and Y.B. Rutickii, "Convex functions and Orlicz spaces", Fizmatgiz, Moskva [In Russian; English translation, Noordho_, Groningen], (1961).
    6. W.M. Koslowski, Modular function spaces, Dekker: New York, Basel, (1988).
    7. J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. Vol. 1034 , Springer-verlag, Berlin, 1983.
    8. I.D. Arandelovi_c, "on a fixed point theorem of Kirk", J. Math. Anal. Appl., Vol.301, No. 2, (2005), pp.384-385.
    9. M. Edelstein, "On fixed and periodic points under contractive mappings", J. London Math. Soc., Vol. 37, No. 1, (1962), pp.74-79.
    10. L.B _ Ciri_c, "A generalization of Banach's contraction principle", Proc. Amer. Math. Soc., 45(2) (1974), pp.267-273.
    11. E. Rakotch, "A note on contractive mappings", Proc. Amer. Math. Soc., Vol. 13, No. 3, (1962), pp.459-465.
    12. S. Reich, "Fixed points of contractive functions", Bollettino dell'Unione Mathematica Italiana, Vol. 4, No. 5, (1972), pp. 26-42.
    13. W.A. Kirk, contraction mappings and extensions, Handbook of Metric Fixed Point Theory, W.A. Kirk and B. Sims, Eds. Kluwer Academic Publishers, Dordrecht, The Netherlands, (2001), pp.1-34.
    14. A. Razani, E. Nabizadeh, M. Beyg Mohamadi and S. Homaei Pour, "Fixed points of nonlinear and asymptotic contraction in modular spaces", Abs. Appl. Anal., Vol. 2007, (2007), Article ID 40575, 10 pages. http://www.journalo_nequalitiesandapplications.com/content/2013/1/399.
    15. M. A. Khamsi, "Quasicontraction Mapping in modular spaces without _2-condition", Fixed Point Theory and Applications, Vol. 2008, (2008), Artical ID 916187, 6 pages. http://www._xedpointtheoryandapplications.com/content/pdf/1687-1812-2008-916187.
    16. K. Kuaket and P. Kumam, "Fixed point of asymptotic pointwise contractions in modular spaces", Appl. Math. Letters, Vol. 24, (2011), pp.1795-1798.
    17. X. Wang and Y. Chen, "Fixed points of asymptotic pointwise nonexpansive mappings in modular spaces", J. Appl. Math., Vol. 2012, (2012), Article ID 319394, 6 pages. http://www.emis.de/journals/HOA/JAM/Volume2012/319394.
    18. I. Alton, M. Abbas and H. Simsek, "A _xed point theorem on cone metric spaces with new type contractivity", Banach J. Math. Anal., Vol. 5, No. 2, (2011), pp.15-24.

 

View

Download

Article ID: 3738
 
DOI: 10.14419/ijamr.v3i4.3738




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.