Some Remarks on G-Metric Spaces and Fixed Point Theorems

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Vesna Cojbasic Rajic

Abstract

We notice some remarks on G-metric spaces and the fixed point results of contractive mappings defined on such spaces. Our results generalize, extend and complement recent fixed point theorems established by   Jleli and Samet [M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl. 2012:210 (2012)].

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References

  1. M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications 341(1), 416-420 (2008)
  2. R.Agarwal, E.Karapinar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory and Applications 2013:2, (2013)
  3. D. Doitchinov, On completness in quasi-metric spaces,Topology and its Applications 30,127-148 (1988)
  4. M. Jleli, V. ĆojbaÅ¡ić Rajić, B. Samet and C. Vetro, Fixed point theorems on ordered metric spaces and applications to nonlinear beam equations, Journal of Fixed Point Theory and its Applications, doi: 10.1007/s11784-012-0081-4 (2012)
  5. M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl. 2012:210 (2012)
  6. Z. Kadelburg, H. K. Nashine and S. Radenović, Common coupled fixed point results in partially ordered G-metric spaces, Bulletin of Mathematical Analysis and applications 4(2), 51-63 (2012)
  7. E. Karapinar, R. P. Agarwal, Further Remarks on G-metric spaces, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-154, 2013:154 (2013)
  8. Z. Mustafa, A new structure for generalized metric spaces-with applications to fixed point theory. PhD thesis, the University of Newcastle, Australia (2005)
  9. Z. Mustafa, M. Khandaqji, W. Shatanawi, Fixed Point Results on Complete G-metric spaces, Studia Scientiarum Mathematicarum Hungarica 48, 304-319 (2011)
  10. Z. Mustafa, Z, H. Obiedat, A fixed point theorem of Reich in G-metric spaces. CUBO 12(1), 83-93 (2010)
  11. Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl, Vol 2008, Article ID 189870, 12 pages, (2008)
  12. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2), 289-297 (2006)
  13. Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl, Vol 2009, Article ID 917175, 10 pages, (2009)
  14. Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed point results in G-metric spaces. Int. J. Math. Math. Sci. 2009, Article ID 283028, (2009)
  15. H.Obiedat, Z.Mustafa, Fixed point results on a nonsymmetric G-metric spaces, Jordan Journal of Mathematics and Statistics 3 (2), 65-79 (2010)
  16. S. Radenović, Remarks on some recent coupled coincidence point results in symmetric G-metric spaces, Journal of operators, Vol 2013, Article ID 290525, 8 pages, (2013)
  17. S. Radenović, Z. Kadelburg, D. Jandrlić, A. Jandrlić, Some results on weakly contractive maps, Bulletin of the Iranian Mathematical Society 38 (3), 625-645 (2012)
  18. B. Samet, C. Vetro, F. Vetro, Remarks on G-metric spaces, Int. J. Anal., 2013 (2013), Article ID 917158, 6 pages.
  19. W. Shatanawi, Fixed point theory for contractive mappings satisfying ï¦-maps in G-metric spaces. Fixed Point Theory Appl. 2010, Article ID 181650 (2010)
  20. W. Shatanawi, Some fixed point theorems in ordered G-metric spaces and applications. Abstr. Appl. Anal. 2011, Article ID 126205 (2011)