Research Article
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On partial metric spaces and partial cone metric spaces

Year 2017, Volume: 46 Issue: 6, 1069 - 1075, 01.12.2017
https://izlik.org/JA97HR74WA

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
https://izlik.org/JA97HR74WA

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 Research Article
Authors

Seithuti Moshokoa This is me

Publication Date December 1, 2017
IZ https://izlik.org/JA97HR74WA
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. https://izlik.org/JA97HR74WA
AMA 1.Moshokoa S. On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1069-1075. https://izlik.org/JA97HR74WA
Chicago Moshokoa, Seithuti. 2017. “On Partial Metric Spaces and Partial Cone Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 46 (6): 1069-75. https://izlik.org/JA97HR74WA.
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 [1]S. Moshokoa, “On partial metric spaces and partial cone metric spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, pp. 1069–1075, Dec. 2017, [Online]. Available: https://izlik.org/JA97HR74WA
ISNAD Moshokoa, Seithuti. “On Partial Metric Spaces and Partial Cone Metric Spaces”. Hacettepe Journal of Mathematics and Statistics 46/6 (December 1, 2017): 1069-1075. https://izlik.org/JA97HR74WA.
JAMA 1.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, Dec. 2017, pp. 1069-75, https://izlik.org/JA97HR74WA.
Vancouver 1.Seithuti Moshokoa. On partial metric spaces and partial cone metric spaces. Hacettepe Journal of Mathematics and Statistics [Internet]. 2017 Dec. 1;46(6):1069-75. Available from: https://izlik.org/JA97HR74WA