In: Mathematica Slovaca, vol. 63, no. 3
Pratulananda Das - Sanjoy Ghosal - Sudip Kumar Pal
Details:
Year, pages: 2013, 545 - 562
Keywords:
asymmetric metric space, Approximate Metric Axiom
(AMA), ideal, forward and backward $I$ and $I^{*}$-convergence, forward and backward $I$ and $I^{*}$-Cauchy sequences, condition~(AP)
About article:
In this paper we use the notion of ideals to extend the convergence and Cauchy conditions in asymmetric metric spaces. The asymmetry (or rather, absence of symmetry) of these spaces makes the whole treatment different from the metric case and we use a genuinely asymmetric condition called (AMA) to prove many results and show that certain classic results fail in the asymmetric context if the assumption is dropped.
How to cite:
ISO 690:
Das, P., Ghosal, S., Pal, S. 2013. Extending asymmetric convergence and Cauchy condition using ideals. In Mathematica Slovaca, vol. 63, no.3, pp. 545-562. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0117-2
APA:
Das, P., Ghosal, S., Pal, S. (2013). Extending asymmetric convergence and Cauchy condition using ideals. Mathematica Slovaca, 63(3), 545-562. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0117-2
About edition: