KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 1

Generalizations of metrics and partial metrics

Ralph KOPPERMAN
Homeira PAJOOHESH
Sayfa
9–14
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this article we show that much of the theory of metric spaces, including the Banach fixed point theorem extends to these spaces.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In [14] $k$-metric spaces were defined for certain $\ell$-group applications, by weakening the metric triangle inequality.
📊
Temel Bulgular & Veri:In [14] $k$-metric spaces were defined for certain $\ell$-group applications, by weakening the metric triangle inequality.
💡
Sonuç & Katkı:In this article we show that much of the theory of metric spaces, including the Banach fixed point theorem extends to these spaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:partial metrics · variety of $\ell$-groups · $k$-metrics

Abstract

In [14] $k$-metric spaces were defined for certain $\ell$-group applications, by weakening the metric triangle inequality. In this article we show that much of the theory of metric spaces, including the Banach fixed point theorem extends to these spaces.

🔖

Bu Makaleye Atıf Yap

KOPPERMAN, R., PAJOOHESH, H. (2022). Generalizations of metrics and partial metrics. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 1, 9–14. https://ajindex.com/articles/529929

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (14)

  1. Birkho, G., Lattice Theory, 3rd Edition, American Mathematical Society Colloquium Pub- lications, Volume 25, 1967,
  2. Providence, RI. Bukatin, M., Kopperman, R., Matthews, S., and Pajoohesh, H., Partial Metric spaces, American Mathematical Monthly 116, 708-718, 2009.
  3. Darnel, M. and Holland, W.C., Minimal non-metabelian varieties of $\ell$-groups that contain no nonabelian o-groups, Communications in Algebra 42, 5100-5133, 2014.
  4. Darnel, M., Holland, W.C., Pajoohesh, H.,The relationship of partial metric varieties and commuting powers varieties, Order, 30, no.2, 403-414, 2013.
  5. Holland, W. C., Intrinsic metrics for lattice-ordered groups, Algebra Universalis, 19, 142- 150, 1984.
  6. Holland, W.C, Kopperman, R. and Pajoohesh, H., Intrinsic generalized metrics Algebra Universalis, 67, no.1, 1-18, 2012.
  7. Kopperman, R., Lengths on Semigroups and Groups, Semigroup Forum 25, 345-360, 1984.
  8. Kopperman, R., All Topologies Come From Generalized Metrics, Am. Math. Monthly 95, 89-97, 1988.
  9. Kopperman, R., Mynard, F., and Ruse, P., Quasi-metric representations of various cate- gories of closure spaces, Topology Proceedings, 37: 331-347, 2011.
  10. Kopperman, R., Matthews, S., and Pajoohesh, H., Completions of partial metrics into value lattices, Topology and Applications 156, 1534-1544, 2009.
  11. Kopperman, R., Matthews, S., and Pajoohesh, H., Universal partial metrizability, Applied General Topology 5, 115-127 2004.
  12. Matthews, S. G., Partial metric topology", Proc. 8th summer conference on topology and its applications, ed S. Andima et al., New York Academy of Sciences Annals, 728, 183-197, 1994.
  13. Pajoohesh, H., The relationship of partial metric varieties and commuting powers varieties II, Algebra Universalis, 73, issue 3-4, 291-295, 2015.
  14. Pajoohesh, H., k-metric spaces, Algebra Universalis, 69, no.1, 27-43, 2013.