On some Zeweir I-convergent sequence spaces defined by a modulus function
详细信息 查看全文
- 作者：Vakeel A. Khan (1)
Khalid Ebadullah (1)
Ayhan Esi (2)
Mohd Shafiq (1)
1. Department of Mathematics ; A.M.U. ; Aligarh ; 202002 ; India
2. Department of Mathematics ; Science and Art Faculty ; Adiyaman University ; 02040聽 ; Adiyaman ; Turkey - 关键词：Ideal ; Filter ; Modulus function ; Lipschitz function ; I ; convergence field ; I ; convergent ; Monotone and solid spaces ; 40A05 ; 40A35 ; 40C05 ; 46A45
- 刊名：Afrika Matematika
- 出版年：2015
- 出版时间：March 2015
- 年：2015
- 卷：26
- 期：1-2
- 页码：115-125
- 全文大小：172 KB
- 参考文献：1. Ba艧ar, F., Altay, B.: On the spaces of sequences of p-bounded variation and related matrix mappings. krainion Math. J. 55, 136鈥?47 (2003)
2. Buck, R.C.: Generalized asymptotic density. Am. J. Math. 75, 335鈥?46 (1953) CrossRef
3. Connor, J.S.: The statistical and strong P-Cesaro convergence of sequences. Analysis 8, 47鈥?3 (1988) CrossRef
4. Connor, J.S.: On strong matrix summability with respect to a modulus and statistical convergence. Cnad. Math. Bull. 32, 194鈥?98 (1989) CrossRef
5. Connor, J., Kline, J.: On statistical limit points and the consistency of statistical convergence. J. Math. Anal. Appl. 197, 392鈥?99 (1996) CrossRef
6. Connor, J., Fridy, J.A., Kline, J.: Statistically pre-Cauchy sequence. Analysis 14, 311鈥?17 (1994) CrossRef
7. Demirci, K.: I-limit superior and limit inferior. Math. Commun. 6, 165鈥?72 (2001)
8. Dems, K.: On I-Cauchy sequences. Real Anal. Exch. 30, 123鈥?28 (2005)
9. Fast, H.: Surla convergence statistique. Colloq. Math. 2, 241鈥?44 (1951)
10. Fridy, J.A.: On statistical convergence. Analysis 5, 301鈥?13 (1985) CrossRef
11. Fridy, J.A.: Statistical limit points. Proc. Am. Math. Soc. 11, 1187鈥?192 (1993) CrossRef
12. Garling, D.J.H.: On symmetric sequence spaces. Proc. Lond. Math. Soc. 16, 85鈥?06 (1966) CrossRef
13. Garling, D.J.H.: Symmetric bases of locally convex spaces. Studia Math. Soc. 30, 163鈥?81 (1968)
14. Gramsch, B.: Die Klasse metrisher linearer Raume L( \(\phi \) ). Math. Ann. 171, 61鈥?8 (1967) CrossRef
15. Gurdal, M.: Some types of convergence. Doctoral dissertation, S.Demirel University, Isparta (2004)
16. Kamthan, P.K., Gupta, M.: Sequence Spaces and Series. Marcel Dekker Inc., New York (1980)
17. Khan, V.A., Ebadullah, K.: On some I-convergent sequence spaces defined by a modulus function. Theory Appl. Math. Comput. Sci. 1(2), 22鈥?0 (2011)
18. Khan, V.A., Ebadullah, K., Ahmad, A.: I-pre-Cauchy sequences and Orlicz function. J. Math. Anal. 3(1), 21鈥?6 (2012)
19. Khan, V.A., Ebadullah, K.: I-convergent difference sequence spaces defined by a sequence of moduli. J. Math. Comput. Sci. 2(2), 265鈥?73 (2012)
20. Khan, V.A., Ebadullah, K.: On Zweier I-convergent sequence spaces. Submitted (2013)
21. Kostyrko, P., 艩al谩t, T., Wilczy艅ski, W.: I-convergence. Real Anal. Exch. 26(2), 669鈥?86 (2000)
22. K枚the, G.: Topological Vector spaces 1. Springer, Berlin (1970)
23. Malkowsky, E.: Recent results in the theory of matrix transformation in sequence spaces. Math. Vesnik. 49, 187鈥?96 (1997)
24. Nakano, H.: Concave modulars. J. Math. Soc. Jpn. 5, 29鈥?9 (1953) CrossRef
25. Ng, P., Lee, P,Y.: Cesaro sequence spaces of non-absolute type. Comment. Math. Practice Math. 20(2), 429鈥?33 (1978)
26. Ruckle, W.H.: On perfect symmetric BK-spaces. Math. Ann. 175, 121鈥?26 (1968) CrossRef
27. Ruckle, W.H.: Symmetric coordinate spaces and symmetric bases. Canad. J. Math 19, 828鈥?38 (1967) CrossRef
28. Ruckle, W.H.: FK-spaces in which the sequence of coordinate vectors is bounded. Canad. J. Math 25(5), 973鈥?75 (1973) CrossRef
29. 艩al谩t, T.: On statisticaly convergent sequences of real numbers. Math. Slovaca 30, 139鈥?50 (1980)
30. 艩al谩t, T., Tripathy, B.C., Ziman, M.: On some properties of I-convergence. Tatra Mt. Math. Publ. 28, 279鈥?86 (2004)
31. 艩al谩t, T., Tripathy, B.C., Ziman, M.: On I-convergence field. Ital. J. Pure Appl. Math. 17, 45鈥?4 (2005)
32. Schoenberg, I.J.: The integrability of certain functions and related summability methods. Am. Math. Mon. 66, 361鈥?75 (1959) CrossRef
33. 艦eng枚n眉l, M.: On the Zweier sequence space. Demonstratio Math. XL(1), 181鈥?96 (2007)
34. Tripathy, B.C., Hazarika, B.: Paranorm I-convergent sequence spaces. Math. Slovaca 59(4), 485鈥?94 (2009) CrossRef
35. Tripathy, B.C., Hazarika, B.: Some I-convergent sequence spaces defined by Orlicz function. Acta Math. Appl. Sin. 27(1), 149鈥?54 (2011) CrossRef
36. Tripathy, B.C., Hazarika, B.: I-convergent sequence spaces associated with multiplier sequence spaces. Math. Inequal. Appl. 11(3), 543鈥?48 (2008)
37. Tripathy, B.C., Hazarika, B.: I-monotonic and I-convergent sequences. Kyungpook Math. J. 51(2), 233鈥?39 (2011) CrossRef
38. Tripathy, B.C., Sen, M., Nath, S.: I-convergence in probabilistic n-normed space. Soft Comput. 16, 1021鈥?027 (2012). doi:10.1007/s00500-011-0799-8
39. Tripathy, B.C., Sharma, B.: On I-convergent double sequences of fuzzy real numbers. Kyungpook Math. J. 52(2), 189鈥?00 (2012) CrossRef
40. Tripathy, B.C., Mahanta, S.: On I-acceleration convergence of sequences. J. Frankl. Inst. 347, 591鈥?98 (2010) CrossRef
41. Tripathy, B.C., Dutta, A.J.: On I-acceleration convergence of sequences of fuzzy real numbers. Math. Modell. Anal. 17(4), 549鈥?57 (2012) CrossRef
42. Tripathy, B.C., Hazarika, B., Choudhary, B.: Lacunary I-convergent sequences. Kyungpook Math. J. 52(4), 473鈥?82 (2012) CrossRef
43. Tripathy, B.C., Chandra, P.: On some generalized difference paranormed sequence spaces associated with multiplier sequences defined by modulus function. Anal. Theory Appl. 27(1), 21鈥?7 (2011) CrossRef
44. Wang, C.S.: On N枚rlund sequence spaces. Tamkang J. Math. 9, 269鈥?74 (1978) - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics Education
Applications of Mathematics
History of Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：2190-7668
文摘
In this article we introduce the sequence spaces \(\mathcal Z ^{I}(f)\) , \(\mathcal Z ^{I}_{0}(f)\) and \(\mathcal Z ^{I}_{\infty }(f)\) for a modulus function \(f\) and study some of the topological and algebraic properties on these spaces.