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Abstrakty
The concepts of I-convergence and I-Cauchy condition are a generalization of statistical convergence and statistical Cauchy conditions and are dependent on the notion of the ideal I of subsets of the set N of positive integers. In this paper, we shall introduce two new notions of I-uniform continuity and I-uniform boundedness of a function with values in R or in a metric space and then study their basic properties.
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
887--894
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Faculty Of Science, Department Of Mathematics Kalyani Government Engineering College Kalyani, Nadia-741235 West Bengal, India, sanjoykrghosal@yahoo.co.in
Bibliografia
- [1] V. Balaz, J. Cervenansky, P. Kostyrko, T. Šalát, I -convergence and I -continuity of real functions, Acta. Math (Nitra) 5 (2002), 43–50.
- [2] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007), 715–729.
- [3] P. Das, S. Ghosal, Some further results on I -Cauchy sequence and condition (AP), Comput. Math. Appl. 59 (2010), 2597–2600.
- [4] K. Dems, On I -Cauchy sequences, Real Anal. Exchange 30(1) (2004–2005), 123–128.
- [5] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
- [6] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
- [7] S. Ghosal, Some further results on I -uniform continuity and I -uniform boundedness of a function, communicated.
- [8] M. Gurdal, Some type of convergence, Doctoral Diss., S. Demirel Univ., Isparta, 2004.
- [9] P. Kostyrko, T. Šalát, W. Wilczynski, I -convergence, Real Anal. Exchange 26(2) (2000/2001), 669–685.
- [10] P. Kostyrko, M. Macaj, T. Šalát, M. Sleziak, I -convergence and extremal I –limit points, Math. Slovaca 55 (2005), 443–464.
- [11] A. Nabiev, S. Pehlivan, M. Gurdal, On I -Cauchy sequences, Taiwanese J. Math. 11(2) (2007), 569–576.
- [12] S. Pehlivan, M. A. Mamedov, Statistical cluster points and turnpike, Optimization, 48 (2000), 93–106.
- [13] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
- [14] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375.
- [15] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0035-0030