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Yıl 2020, Cilt: 33 Sayı: 3, 761 - 765, 01.09.2020

Çetin Cemal Özeken Cüneyt Çevik

https://doi.org/10.35378/gujs.604784
Cited By: 2

Öz

Kaynakça

  • [1] H. Nakano, Ergodic theorems in semi-ordered linear spaces, Ann. Math. 49 (1948), 538-556.
  • [2] R. DeMarr, Partially ordered linear spaces and locally convex linear topological spaces, Illinois J. Math., 8 (1964), 601--606.
  • [3] S. Kaplan, On unbounded order convergence, Real Anal. Exchange, 23 (1) (1998-99), 175-184.
  • [4] N. Gao and F. Xanthos, Unbounded order convergence and application to martingales without probability, J. Math. Anal. Appl., 415 (2) (2014), 931--947.
  • [5] N. Gao, V. G. Troitsky, and F. Xanthos, Uo-convergence and its applications to cesáro means in banach lattices, Israel Journal of Math., 220 (2017), 649-689.
  • [6] C. D. Aliprantis and O. Burkinshaw, Positive operators, Springer, Dordrecht, 2006.
  • [7] W. A. J. Luxemburg and A. C. Zaanen, Riesz Space I, North-Holland, Amsterdam, The Netherland, 1971.
  • [8] C. Çevik and I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34 (2), (2009), 375--382.

Unbounded Vectorial Cauchy Completion of Vector Metric Spaces

Yıl 2020, Cilt: 33 Sayı: 3, 761 - 765, 01.09.2020

Çetin Cemal Özeken Cüneyt Çevik

https://doi.org/10.35378/gujs.604784
Cited By: 2

Öz

A sequence (an) in a Riesz space E is called uo-convergent (or unbounded order convergent) to a in E if  inf{|an-a|,u} is order convergent to 0 for all u in E+ and
unbounded order Cauchy (uo-Cauchy) if |an-an+p|is
uo-convergent to 0. In the first part of this study we define ud,E-convergence
(or unbounded vectorial convergence) in vector metric spaces, which is more
general than usual metric spaces, and examine relations between unbounded order
convergence, unbounded vectorial convergence, vectorial convergence and order
convergence. In the last part we construct the unbounded Cauchy completion of
vector metric spaces by the motivation of the fact that every metric space has
Cauchy completion. In this way, we have obtained a more general completion of
vector metric spaces.


Anahtar Kelimeler

Unbounded order convergence vector metric spaces unbounded vectorial convergence unbounded Cauchy completion Riesz space

Kaynakça

  • [1] H. Nakano, Ergodic theorems in semi-ordered linear spaces, Ann. Math. 49 (1948), 538-556.
  • [2] R. DeMarr, Partially ordered linear spaces and locally convex linear topological spaces, Illinois J. Math., 8 (1964), 601--606.
  • [3] S. Kaplan, On unbounded order convergence, Real Anal. Exchange, 23 (1) (1998-99), 175-184.
  • [4] N. Gao and F. Xanthos, Unbounded order convergence and application to martingales without probability, J. Math. Anal. Appl., 415 (2) (2014), 931--947.
  • [5] N. Gao, V. G. Troitsky, and F. Xanthos, Uo-convergence and its applications to cesáro means in banach lattices, Israel Journal of Math., 220 (2017), 649-689.
  • [6] C. D. Aliprantis and O. Burkinshaw, Positive operators, Springer, Dordrecht, 2006.
  • [7] W. A. J. Luxemburg and A. C. Zaanen, Riesz Space I, North-Holland, Amsterdam, The Netherland, 1971.
  • [8] C. Çevik and I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34 (2), (2009), 375--382.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

Çetin Cemal Özeken Bu kişi benim 0000-0002-5916-0688

Cüneyt Çevik 0000-0001-9516-0100

Yayımlanma Tarihi 1 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 33 Sayı: 3

Kaynak Göster

APA Özeken, Ç. C., & Çevik, C. (2020). Unbounded Vectorial Cauchy Completion of Vector Metric Spaces. Gazi University Journal of Science, 33(3), 761-765. https://doi.org/10.35378/gujs.604784
AMA Özeken ÇC, Çevik C. Unbounded Vectorial Cauchy Completion of Vector Metric Spaces. Gazi University Journal of Science. Eylül 2020;33(3):761-765. doi:10.35378/gujs.604784
Chicago Özeken, Çetin Cemal, ve Cüneyt Çevik. “Unbounded Vectorial Cauchy Completion of Vector Metric Spaces”. Gazi University Journal of Science 33, sy. 3 (Eylül 2020): 761-65. https://doi.org/10.35378/gujs.604784.
EndNote Özeken ÇC, Çevik C (01 Eylül 2020) Unbounded Vectorial Cauchy Completion of Vector Metric Spaces. Gazi University Journal of Science 33 3 761–765.
IEEE Ç. C. Özeken ve C. Çevik, “Unbounded Vectorial Cauchy Completion of Vector Metric Spaces”, Gazi University Journal of Science, c. 33, sy. 3, ss. 761–765, 2020, doi: 10.35378/gujs.604784.
ISNAD Özeken, Çetin Cemal - Çevik, Cüneyt. “Unbounded Vectorial Cauchy Completion of Vector Metric Spaces”. Gazi University Journal of Science 33/3 (Eylül 2020), 761-765. https://doi.org/10.35378/gujs.604784.
JAMA Özeken ÇC, Çevik C. Unbounded Vectorial Cauchy Completion of Vector Metric Spaces. Gazi University Journal of Science. 2020;33:761–765.
MLA Özeken, Çetin Cemal ve Cüneyt Çevik. “Unbounded Vectorial Cauchy Completion of Vector Metric Spaces”. Gazi University Journal of Science, c. 33, sy. 3, 2020, ss. 761-5, doi:10.35378/gujs.604784.
Vancouver Özeken ÇC, Çevik C. Unbounded Vectorial Cauchy Completion of Vector Metric Spaces. Gazi University Journal of Science. 2020;33(3):761-5.

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