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Generalizations of metrics and partial metrics

Yıl 2017, Cilt: 46 Sayı: 1, 9 - 14, 01.02.2017

Öz

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.

Kaynakça

  • Birkho, G., Lattice Theory, 3rd Edition, American Mathematical Society Colloquium Pub- lications, Volume 25, 1967, Providence, RI.
  • Bukatin, M., Kopperman, R., Matthews, S., and Pajoohesh, H., Partial Metric spaces, American Mathematical Monthly 116, 708-718, 2009.
  • 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.
  • Darnel, M., Holland, W.C., Pajoohesh, H.,The relationship of partial metric varieties and commuting powers varieties, Order, 30, no.2, 403-414, 2013.
  • Holland, W. C., Intrinsic metrics for lattice-ordered groups, Algebra Universalis, 19, 142- 150, 1984.
  • Holland, W.C, Kopperman, R. and Pajoohesh, H., Intrinsic generalized metrics Algebra Universalis, 67, no.1, 1-18, 2012.
  • Kopperman, R., Lengths on Semigroups and Groups, Semigroup Forum 25, 345-360, 1984.
  • Kopperman, R., All Topologies Come From Generalized Metrics, Am. Math. Monthly 95, 89-97, 1988.
  • Kopperman, R., Mynard, F., and Ruse, P., Quasi-metric representations of various cate- gories of closure spaces, Topology Proceedings, 37: 331-347, 2011.
  • Kopperman, R., Matthews, S., and Pajoohesh, H., Completions of partial metrics into value lattices, Topology and Applications 156, 1534-1544, 2009.
  • Kopperman, R., Matthews, S., and Pajoohesh, H., Universal partial metrizability, Applied General Topology 5, 115-127 2004.
  • 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.
  • Pajoohesh, H., The relationship of partial metric varieties and commuting powers varieties II, Algebra Universalis, 73, issue 3-4, 291-295, 2015.
  • Pajoohesh, H., k-metric spaces, Algebra Universalis, 69, no.1, 27-43, 2013.
Yıl 2017, Cilt: 46 Sayı: 1, 9 - 14, 01.02.2017

Öz

Kaynakça

  • Birkho, G., Lattice Theory, 3rd Edition, American Mathematical Society Colloquium Pub- lications, Volume 25, 1967, Providence, RI.
  • Bukatin, M., Kopperman, R., Matthews, S., and Pajoohesh, H., Partial Metric spaces, American Mathematical Monthly 116, 708-718, 2009.
  • 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.
  • Darnel, M., Holland, W.C., Pajoohesh, H.,The relationship of partial metric varieties and commuting powers varieties, Order, 30, no.2, 403-414, 2013.
  • Holland, W. C., Intrinsic metrics for lattice-ordered groups, Algebra Universalis, 19, 142- 150, 1984.
  • Holland, W.C, Kopperman, R. and Pajoohesh, H., Intrinsic generalized metrics Algebra Universalis, 67, no.1, 1-18, 2012.
  • Kopperman, R., Lengths on Semigroups and Groups, Semigroup Forum 25, 345-360, 1984.
  • Kopperman, R., All Topologies Come From Generalized Metrics, Am. Math. Monthly 95, 89-97, 1988.
  • Kopperman, R., Mynard, F., and Ruse, P., Quasi-metric representations of various cate- gories of closure spaces, Topology Proceedings, 37: 331-347, 2011.
  • Kopperman, R., Matthews, S., and Pajoohesh, H., Completions of partial metrics into value lattices, Topology and Applications 156, 1534-1544, 2009.
  • Kopperman, R., Matthews, S., and Pajoohesh, H., Universal partial metrizability, Applied General Topology 5, 115-127 2004.
  • 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.
  • Pajoohesh, H., The relationship of partial metric varieties and commuting powers varieties II, Algebra Universalis, 73, issue 3-4, 291-295, 2015.
  • Pajoohesh, H., k-metric spaces, Algebra Universalis, 69, no.1, 27-43, 2013.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Ralph Kopperman Bu kişi benim

Homeira Pajoohesh Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 1

Kaynak Göster

APA Kopperman, R., & Pajoohesh, H. (2017). Generalizations of metrics and partial metrics. Hacettepe Journal of Mathematics and Statistics, 46(1), 9-14.
AMA Kopperman R, Pajoohesh H. Generalizations of metrics and partial metrics. Hacettepe Journal of Mathematics and Statistics. Şubat 2017;46(1):9-14.
Chicago Kopperman, Ralph, ve Homeira Pajoohesh. “Generalizations of Metrics and Partial Metrics”. Hacettepe Journal of Mathematics and Statistics 46, sy. 1 (Şubat 2017): 9-14.
EndNote Kopperman R, Pajoohesh H (01 Şubat 2017) Generalizations of metrics and partial metrics. Hacettepe Journal of Mathematics and Statistics 46 1 9–14.
IEEE R. Kopperman ve H. Pajoohesh, “Generalizations of metrics and partial metrics”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 1, ss. 9–14, 2017.
ISNAD Kopperman, Ralph - Pajoohesh, Homeira. “Generalizations of Metrics and Partial Metrics”. Hacettepe Journal of Mathematics and Statistics 46/1 (Şubat 2017), 9-14.
JAMA Kopperman R, Pajoohesh H. Generalizations of metrics and partial metrics. Hacettepe Journal of Mathematics and Statistics. 2017;46:9–14.
MLA Kopperman, Ralph ve Homeira Pajoohesh. “Generalizations of Metrics and Partial Metrics”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 1, 2017, ss. 9-14.
Vancouver Kopperman R, Pajoohesh H. Generalizations of metrics and partial metrics. Hacettepe Journal of Mathematics and Statistics. 2017;46(1):9-14.