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On partial metric spaces and partial cone metric spaces

Year 2017, Volume: 46 Issue: 6, 1069 - 1075, 01.12.2017

Abstract

It this article we shall show that partial metric spaces and partial cone metric spaces are quasi-uniformizable and hence quasi-metrizable. Finally,
an application to the Banach’s fixed point theorem will be presented in this context.

References

  • T. Abdeljawad, Quasi cone metric spaces and generalizations of Caristi Kirk’s theorem, Fixed Point Theory and its Applications, 9 pages, ID 574387, 2009.
  • M. Asadi, B.E. Rhoades, H. Soleimani, Some note on the paper " The equivalence of cone metric spaces and metric spaces, Fixed point theory and applications, 87, 1 - 4, 2012.
  • W-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72, 2259 - 2261, 2010.
  • Z. Ercan, On the end of the cone metric spaces, Topology and its Applications, 166, 10-14, 2014.
  • P. Fletcher, W. F. Lindgren, Quasi uniform spaces, Marcel Dekker Inc., New York, 1982.
  • R. H. Haghi, Sh. Rezapour, N. Shahad, Be careful on partial metric fixed point results, Topopoly and its Applications 160, 450-454, 2013.
  • X. Ge, S. Lin, Completions of partial metric spaces, Topology and its Applications, 182, 16-23, 2015.
  • R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Cat. Struct. 7, 71 - 83, 1999.
  • S. G. Matthews, Partial metric topology, in: Proceedings of the 8th Summer Conference on General Topology and its Applications, Ann. New York Acad. Sci. 728, 183-196, 1994.
  • S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and its Applications, vol 2010, Article ID 493298,6 pages, 2010.
  • S. Romaguera, O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Science, 19, 541-563, 2009.
  • F. Shadda, M. S. MD Noorani, Fixed point results in quasi cone metric spaces, Abstract and Applied Analysis, Vol 2013, Article ID 303626 7 pages, 2013.
  • A. Sonmez, Fixed point theorems in partial cone metric space, arXiv:1101.2741v1, 2011.
Year 2017, Volume: 46 Issue: 6, 1069 - 1075, 01.12.2017

Abstract

References

  • T. Abdeljawad, Quasi cone metric spaces and generalizations of Caristi Kirk’s theorem, Fixed Point Theory and its Applications, 9 pages, ID 574387, 2009.
  • M. Asadi, B.E. Rhoades, H. Soleimani, Some note on the paper " The equivalence of cone metric spaces and metric spaces, Fixed point theory and applications, 87, 1 - 4, 2012.
  • W-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72, 2259 - 2261, 2010.
  • Z. Ercan, On the end of the cone metric spaces, Topology and its Applications, 166, 10-14, 2014.
  • P. Fletcher, W. F. Lindgren, Quasi uniform spaces, Marcel Dekker Inc., New York, 1982.
  • R. H. Haghi, Sh. Rezapour, N. Shahad, Be careful on partial metric fixed point results, Topopoly and its Applications 160, 450-454, 2013.
  • X. Ge, S. Lin, Completions of partial metric spaces, Topology and its Applications, 182, 16-23, 2015.
  • R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Cat. Struct. 7, 71 - 83, 1999.
  • S. G. Matthews, Partial metric topology, in: Proceedings of the 8th Summer Conference on General Topology and its Applications, Ann. New York Acad. Sci. 728, 183-196, 1994.
  • S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and its Applications, vol 2010, Article ID 493298,6 pages, 2010.
  • S. Romaguera, O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Science, 19, 541-563, 2009.
  • F. Shadda, M. S. MD Noorani, Fixed point results in quasi cone metric spaces, Abstract and Applied Analysis, Vol 2013, Article ID 303626 7 pages, 2013.
  • A. Sonmez, Fixed point theorems in partial cone metric space, arXiv:1101.2741v1, 2011.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Seithuti Moshokoa This is me

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 6

Cite

APA Moshokoa, S. (2017). On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics, 46(6), 1069-1075.
AMA Moshokoa S. On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics. December 2017;46(6):1069-1075.
Chicago Moshokoa, Seithuti. “On Partial Metric Spaces and Partial Cone Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 46, no. 6 (December 2017): 1069-75.
EndNote Moshokoa S (December 1, 2017) On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics 46 6 1069–1075.
IEEE S. Moshokoa, “On partial metric spaces and partial cone metric spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, pp. 1069–1075, 2017.
ISNAD Moshokoa, Seithuti. “On Partial Metric Spaces and Partial Cone Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 46/6 (December 2017), 1069-1075.
JAMA Moshokoa S. On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics. 2017;46:1069–1075.
MLA Moshokoa, Seithuti. “On Partial Metric Spaces and Partial Cone Metric Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, 2017, pp. 1069-75.
Vancouver Moshokoa S. On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1069-75.