Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 5, 1466 - 1476, 15.10.2021
https://doi.org/10.15672/hujms.815689

Öz

Kaynakça

  • [1] G. Beer and M.I. Garrido, Bornologies and locally Lipschitz functions, Bull. Aust. Math. Soc. 90, 257–263, 2014.
  • [2] G. Beer and S. Levi, Total boundedness and bornologies, Topology Appl. 156, 1271– 1288, 2009.
  • [3] G. Beer and S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350, 568–589, 2009.
  • [4] S. Cobzas, Completeness in Quasi-Pseudometric SpacesA Survey, Mathematics, 8 (8), 1279, 2020.
  • [5] S. Cobzas, Functional analysis in asymmetric normed spaces, Frontiers in Mathemat- ics, Springers, Basel, 2013.
  • [6] G. Di Maio, E. Meccariello and S. Naimpally, Decompositions of UC spaces, Questions Answers Gen. Topology, 22, 13–22, 2004.
  • [7] D. Doitchinov, On completeness in quasi-metric spaces, Topology Appl. 30, 127–148, 1988.
  • [8] T. Jain and S. Kundu, Atsuji completions: Equivalent characterisations, Topology Appl. 154, 28–38, 2007.
  • [9] H-P.A. Künzi, An introduction to quasi-uniform spaces, Contemp. Math. 486, 239– 304, 2009.
  • [10] S.P. Moshokoa, On classes of maps with the extension property to the bicompletion in quasi-pseudo metric spaces, Quaest. Math. 28, 391–400, 2005.
  • [11] O. Olela Otafudu, W. Toko and D. Mukonda, On bornology of extended quasi-metric spaces, Hacet. J. Math. Stat. 48, 1767–1777, 2019.
  • [12] R.F. Snipes, Functions that preserve Cauchy sequences, Nieuw Arch. Voor Wiskd. 25, 409–422, 1977.
  • [13] I.L. Reilly, P.V. Subrahmanyam and M.K. Vamanamurthy, Cauchy sequences in quasi-pseudometric spaces, Monatsh. Math. 93, 127–140, 1982.
  • [14] S. Romaguera and M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98, 311–322, 1999.
  • [15] S. Romaguera and P. Tirado, A characterization of quasi-metric completeness in terms of -contractive mappings having fixed points, Mathematics, 8 (1), 16, 2020.
  • [16] T. Vroegrijk, Pointwise bornological space, Topology Appl. 156, 2019–2027, 2009.

Maps that preserve left (right) $K$-Cauchy sequences

Yıl 2021, Cilt: 50 Sayı: 5, 1466 - 1476, 15.10.2021
https://doi.org/10.15672/hujms.815689

Öz

 It is well-known that on quasi-pseudometric space $(X,q)$, every $q^s$-Cauchy sequence is left (or right) $K$-Cauchy sequence but the converse does not hold in general. In this article, we study a class of maps that preserve left (right) $K$-Cauchy sequences that we call left (right) $K$-Cauchy sequentially-regular maps. Moreover, we characterize totally bounded sets on a quasi-pseudometric space in terms of maps that preserve left $K$-Cauchy and right $K$-Cauchy sequences and uniformly locally semi-Lipschitz maps.

Kaynakça

  • [1] G. Beer and M.I. Garrido, Bornologies and locally Lipschitz functions, Bull. Aust. Math. Soc. 90, 257–263, 2014.
  • [2] G. Beer and S. Levi, Total boundedness and bornologies, Topology Appl. 156, 1271– 1288, 2009.
  • [3] G. Beer and S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350, 568–589, 2009.
  • [4] S. Cobzas, Completeness in Quasi-Pseudometric SpacesA Survey, Mathematics, 8 (8), 1279, 2020.
  • [5] S. Cobzas, Functional analysis in asymmetric normed spaces, Frontiers in Mathemat- ics, Springers, Basel, 2013.
  • [6] G. Di Maio, E. Meccariello and S. Naimpally, Decompositions of UC spaces, Questions Answers Gen. Topology, 22, 13–22, 2004.
  • [7] D. Doitchinov, On completeness in quasi-metric spaces, Topology Appl. 30, 127–148, 1988.
  • [8] T. Jain and S. Kundu, Atsuji completions: Equivalent characterisations, Topology Appl. 154, 28–38, 2007.
  • [9] H-P.A. Künzi, An introduction to quasi-uniform spaces, Contemp. Math. 486, 239– 304, 2009.
  • [10] S.P. Moshokoa, On classes of maps with the extension property to the bicompletion in quasi-pseudo metric spaces, Quaest. Math. 28, 391–400, 2005.
  • [11] O. Olela Otafudu, W. Toko and D. Mukonda, On bornology of extended quasi-metric spaces, Hacet. J. Math. Stat. 48, 1767–1777, 2019.
  • [12] R.F. Snipes, Functions that preserve Cauchy sequences, Nieuw Arch. Voor Wiskd. 25, 409–422, 1977.
  • [13] I.L. Reilly, P.V. Subrahmanyam and M.K. Vamanamurthy, Cauchy sequences in quasi-pseudometric spaces, Monatsh. Math. 93, 127–140, 1982.
  • [14] S. Romaguera and M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98, 311–322, 1999.
  • [15] S. Romaguera and P. Tirado, A characterization of quasi-metric completeness in terms of -contractive mappings having fixed points, Mathematics, 8 (1), 16, 2020.
  • [16] T. Vroegrijk, Pointwise bornological space, Topology Appl. 156, 2019–2027, 2009.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Olivier Olela Otafudu 0000-0001-9593-7899

Yayımlanma Tarihi 15 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 5

Kaynak Göster

APA Olela Otafudu, O. (2021). Maps that preserve left (right) $K$-Cauchy sequences. Hacettepe Journal of Mathematics and Statistics, 50(5), 1466-1476. https://doi.org/10.15672/hujms.815689
AMA Olela Otafudu O. Maps that preserve left (right) $K$-Cauchy sequences. Hacettepe Journal of Mathematics and Statistics. Ekim 2021;50(5):1466-1476. doi:10.15672/hujms.815689
Chicago Olela Otafudu, Olivier. “Maps That Preserve Left (right) $K$-Cauchy Sequences”. Hacettepe Journal of Mathematics and Statistics 50, sy. 5 (Ekim 2021): 1466-76. https://doi.org/10.15672/hujms.815689.
EndNote Olela Otafudu O (01 Ekim 2021) Maps that preserve left (right) $K$-Cauchy sequences. Hacettepe Journal of Mathematics and Statistics 50 5 1466–1476.
IEEE O. Olela Otafudu, “Maps that preserve left (right) $K$-Cauchy sequences”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 5, ss. 1466–1476, 2021, doi: 10.15672/hujms.815689.
ISNAD Olela Otafudu, Olivier. “Maps That Preserve Left (right) $K$-Cauchy Sequences”. Hacettepe Journal of Mathematics and Statistics 50/5 (Ekim 2021), 1466-1476. https://doi.org/10.15672/hujms.815689.
JAMA Olela Otafudu O. Maps that preserve left (right) $K$-Cauchy sequences. Hacettepe Journal of Mathematics and Statistics. 2021;50:1466–1476.
MLA Olela Otafudu, Olivier. “Maps That Preserve Left (right) $K$-Cauchy Sequences”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 5, 2021, ss. 1466-7, doi:10.15672/hujms.815689.
Vancouver Olela Otafudu O. Maps that preserve left (right) $K$-Cauchy sequences. Hacettepe Journal of Mathematics and Statistics. 2021;50(5):1466-7.