Some Remarks on G-Metric Spaces and Fixed Point Theorems

Cojbasic Rajic, Vesna

Research Article

Some Remarks on G-Metric Spaces and Fixed Point Theorems

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)].

How to Cite

V. Cojbasic Rajic, Some Remarks on G-Metric Spaces and Fixed Point Theorems, Int. J. Anal. Appl. 5 (2014), 102–114.

BibTeX

@article{Rajic2014,
  author  = {Cojbasic Rajic, Vesna},
  title   = {Some Remarks on G-Metric Spaces and Fixed Point Theorems},
  journal = {Int. J. Anal. Appl.},
  volume  = {5},
  year    = {2014},
  pages   = {102--114},
  doi     = {}
}

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 -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)