Abstract
In this paper we introduce and study the concepts of I-divergence and I∗-divergence of sequences as well as double sequences in an asymmetric metric spaces. We investigate the interrelationship between I-divergence and I∗-divergence and show that they are equivalent under some condition and prove some basic properties of these concepts.
References
[1] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl 328(1) (2007), 715–729.10.1016/j.jmaa.2006.05.040Search in Google Scholar
[2] J. Collins, J. Zimmer, An asymmetric Arzela-Ascoli theorem, Top. Appl. 154 (2007), 2312–2322.10.1016/j.topol.2007.03.006Search in Google Scholar
[3] P. Das, S. Ghosal, S. Pal, Extending asymmetric convergence and Cauchy condition through ideals, Math. Slovaca (2011), accepted.Search in Google Scholar
[4] P. Das, S. Ghosal, Some further results on I-Cauchy sequences and condition (AP), Comput. Math. Appl. 59 (2010), 2597–2600.10.1016/j.camwa.2010.01.027Search in Google Scholar
[5] P. Das, P. Kostyrko, W. Wilczyński, P. Malik, I and I∗-convergence of double sequences, Math. Slovaca 58(5) (2008), 605–620.10.2478/s12175-008-0096-xSearch in Google Scholar
[6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.10.4064/cm-2-3-4-241-244Search in Google Scholar
[7] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.10.1524/anly.1985.5.4.301Search in Google Scholar
[8] H. P. A. Kunzi, A note on sequentially compact quasipseudometric spaces, Monatsh. Math. 95(3) (1983), 219–220.10.1007/BF01351999Search in Google Scholar
[9] M. Katetov, Products of filters, Comment. Math. Univ. Carolin. 9 (1968), 173–189.Search in Google Scholar
[10] P. Kostyrko, T. Šalát, W. Wilczyński, I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669–685.10.2307/44154069Search in Google Scholar
[11] A. Mennucci, On asymmetric distances, Technical report, Scuola Normale Superiore, Pisa, 2004.Search in Google Scholar
[12] M. Macaj, T. Šalát, Statistical convergence of subsequences of a given sequence, Math. Bohem. 126 (2001), 191–208.10.21136/MB.2001.133923Search in Google Scholar
[13] A. Nabiev, S. Pehlivan, M. Gurdal, On I-Cauchy sequences, Taiwanese J. Math. 11(2) (2007), 569–576.10.11650/twjm/1500404709Search in Google Scholar
[14] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.Search in Google Scholar
[15] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.10.4064/cm-2-2-98-108Search in Google Scholar
[16] W. A. Wilson, On quasi-metric spaces, Amer. J. Math. 53(3) (1991), 675–684.10.2307/2371174Search in Google Scholar
© 2013 Sanjoy Ghosal et al., published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.