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On the 0-Cauchy Completion of A Partial Metric Space

Year 2016, Volume: 4 , 10 - 15, 13.07.2016

Abstract

It is well known that every metric space admits a Cauchy completion which is unique up to isometry. This result was extended to partial metric spaces, which are generalization of metric spaces. It is the purpose of this paper to construct a 0-Cauchy completion of a partial metric space and we shall show that a 0-Cauchy completion is unique up to isometry. Finally, it is observed that the 0-Cauchy completion of a partial metric space is smaller than its Cauchy completion but coincides with the classical Cauchy completion when restricted to the category of metric spaces.

References

  • Abdeljawad, T., Order norm completions of cone metric spaces, Numerical Functional Analysis and Optimization, 32(2011), 477–495.
  • Abdeljawad, T., Completion of cone metric spaces, Hacettepe Journal of Mathematics and Statistics, 39(2010), 67–74.
  • Chi, K.P., Karapinar, E. and Thanh, T.D., On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces, Bulletin of the Iranian Mathematical Society, 39(2013), 369–381.
  • Chi, K.P., Karapinar, E. and Thanh, T.D., A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55(2012), no:5–6, 1673-1681 doi:10.1016/j.mcm.2011.11.005.
  • Ge, X. and Lin, S., Completions of partial metric spaces, Topology and its Applications, 182(2015), 16–23.
  • Haghi, R.H., Rezapour, S. and Shahzad, N., Be careful on partial metric fixed point results, Topology and its Applications, 160(2013), 450–454.
  • Karapinar, E., Chi, K.P. and Thanh, T.D., A generalization of Ciric quasi-contractions, Abstr. Appl. Anal., 2012(2012), Article ID 518734, 9 pages doi:10.1155/2012/518734.
  • Karapinar, E., Erhan, I.M. and Ulus, A.Y., Fixed point theorem for cyclic maps on partial metric spaces, Appl. Math. Inf. Sci. 6(2012), 239–244.
  • Oltra, S., Romaguera, S. and Sanches-Perez, E., Bicompleting weightable quasi-metric spaces and partial metric spaces, Rend. Circolo Mat. Palermo 51(2002), 151–162.
  • Matthews, S.G., Partial metric topology, in: Proceedings of the 8th Summer Conference on General Topology and its Applications, Ann. New York Acad. Sci. 728(1994), 183–197.
  • Romaguera, S., A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and its Applications, 2010(2010), Article ID 493298, 6 pages.
  • Shoaib, A., Muhammad, A. and Azam, A., From complete dislocated metric space to 0-complete partial metric space, Journal of advanced research in pure mathematics, 72(2015), 89–105.
  • Vetro, C. and Vetro, F., A homotopy fixed point theorem in 0-complete partial metric space, Filomat, 29(2015), 2037–2048.
Year 2016, Volume: 4 , 10 - 15, 13.07.2016

Abstract

References

  • Abdeljawad, T., Order norm completions of cone metric spaces, Numerical Functional Analysis and Optimization, 32(2011), 477–495.
  • Abdeljawad, T., Completion of cone metric spaces, Hacettepe Journal of Mathematics and Statistics, 39(2010), 67–74.
  • Chi, K.P., Karapinar, E. and Thanh, T.D., On the fixed point theorems in generalized weakly contractive mappings on partial metric spaces, Bulletin of the Iranian Mathematical Society, 39(2013), 369–381.
  • Chi, K.P., Karapinar, E. and Thanh, T.D., A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55(2012), no:5–6, 1673-1681 doi:10.1016/j.mcm.2011.11.005.
  • Ge, X. and Lin, S., Completions of partial metric spaces, Topology and its Applications, 182(2015), 16–23.
  • Haghi, R.H., Rezapour, S. and Shahzad, N., Be careful on partial metric fixed point results, Topology and its Applications, 160(2013), 450–454.
  • Karapinar, E., Chi, K.P. and Thanh, T.D., A generalization of Ciric quasi-contractions, Abstr. Appl. Anal., 2012(2012), Article ID 518734, 9 pages doi:10.1155/2012/518734.
  • Karapinar, E., Erhan, I.M. and Ulus, A.Y., Fixed point theorem for cyclic maps on partial metric spaces, Appl. Math. Inf. Sci. 6(2012), 239–244.
  • Oltra, S., Romaguera, S. and Sanches-Perez, E., Bicompleting weightable quasi-metric spaces and partial metric spaces, Rend. Circolo Mat. Palermo 51(2002), 151–162.
  • Matthews, S.G., Partial metric topology, in: Proceedings of the 8th Summer Conference on General Topology and its Applications, Ann. New York Acad. Sci. 728(1994), 183–197.
  • Romaguera, S., A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory and its Applications, 2010(2010), Article ID 493298, 6 pages.
  • Shoaib, A., Muhammad, A. and Azam, A., From complete dislocated metric space to 0-complete partial metric space, Journal of advanced research in pure mathematics, 72(2015), 89–105.
  • Vetro, C. and Vetro, F., A homotopy fixed point theorem in 0-complete partial metric space, Filomat, 29(2015), 2037–2048.
There are 13 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Seithuti Philemon Moshokoa This is me

Publication Date July 13, 2016
Published in Issue Year 2016 Volume: 4

Cite

APA Moshokoa, S. P. (2016). On the 0-Cauchy Completion of A Partial Metric Space. Turkish Journal of Mathematics and Computer Science, 4, 10-15.
AMA Moshokoa SP. On the 0-Cauchy Completion of A Partial Metric Space. TJMCS. July 2016;4:10-15.
Chicago Moshokoa, Seithuti Philemon. “On the 0-Cauchy Completion of A Partial Metric Space”. Turkish Journal of Mathematics and Computer Science 4, July (July 2016): 10-15.
EndNote Moshokoa SP (July 1, 2016) On the 0-Cauchy Completion of A Partial Metric Space. Turkish Journal of Mathematics and Computer Science 4 10–15.
IEEE S. P. Moshokoa, “On the 0-Cauchy Completion of A Partial Metric Space”, TJMCS, vol. 4, pp. 10–15, 2016.
ISNAD Moshokoa, Seithuti Philemon. “On the 0-Cauchy Completion of A Partial Metric Space”. Turkish Journal of Mathematics and Computer Science 4 (July 2016), 10-15.
JAMA Moshokoa SP. On the 0-Cauchy Completion of A Partial Metric Space. TJMCS. 2016;4:10–15.
MLA Moshokoa, Seithuti Philemon. “On the 0-Cauchy Completion of A Partial Metric Space”. Turkish Journal of Mathematics and Computer Science, vol. 4, 2016, pp. 10-15.
Vancouver Moshokoa SP. On the 0-Cauchy Completion of A Partial Metric Space. TJMCS. 2016;4:10-5.