| Title:
|
Lacunary weak statistical convergence (English) |
| Author:
|
Nuray, Fatih |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
259-268 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this work is to generalize lacunary statistical convergence to weak lacunary statistical convergence and $\mathcal I$-convergence to weak $\mathcal I$-convergence. We start by defining weak lacunary statistically convergent and weak lacunary Cauchy sequence. We find a connection between weak lacunary statistical convergence and weak statistical convergence. (English) |
| Keyword:
|
weak convergence |
| Keyword:
|
statistical convergence |
| Keyword:
|
lacunary sequence |
| Keyword:
|
lacunary statistical convergence |
| MSC:
|
40A05 |
| MSC:
|
40A35 |
| MSC:
|
46A25 |
| MSC:
|
46B15 |
| idZBL:
|
Zbl 1249.40004 |
| idMR:
|
MR2893975 |
| DOI:
|
10.21136/MB.2011.141648 |
| . |
| Date available:
|
2011-09-22T14:56:05Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141648 |
| . |
| Reference:
|
[1] Connor, J., Ganichev, M., Kadets, V.: A characterization of Banach spaces with separable duals via weak statistical convergence.J. Math. Anal. Appl. 244 (2000), 251-261. Zbl 0982.46007, MR 1746802, 10.1006/jmaa.2000.6725 |
| Reference:
|
[2] Fridy, J. A.: On statistical convergence.Analysis 5 (1985), 301-313. Zbl 0588.40001, MR 0816582, 10.1524/anly.1985.5.4.301 |
| Reference:
|
[3] Fridy, J. A.: Statistical limit points.Proc. Am. Math. Soc. 118 (1993), 1187-1192. Zbl 0776.40001, MR 1181163, 10.1090/S0002-9939-1993-1181163-6 |
| Reference:
|
[4] Fridy, J. A., Orhan, C.: Lacunary statistical convergence.Pac. J. Math. 160 (1993), 43-51. Zbl 0794.60012, MR 1227502, 10.2140/pjm.1993.160.43 |
| Reference:
|
[5] Fridy, J. A., Orhan, C.: Lacunary statistical summability.J. Math. Anal. Appl. 173 (1993), 497-504. Zbl 0786.40004, MR 1209334, 10.1006/jmaa.1993.1082 |
| Reference:
|
[6] Freedman, A. R., Sember, J. J., Raphael, M.: Some Cesaro type summability spaces.Proc. London Math. Soc., III. Ser. 37 (1978), 508-520. Zbl 0424.40008, MR 0512023 |
| Reference:
|
[7] Freedman, A. R., Sember, J. J.: Densities and summability.Pac. J. Math. 95 (1981), 293-305. Zbl 0504.40002, MR 0632187 |
| Reference:
|
[8] Kostyrko, P., Šalát, T., Wilczyński, W.: $\Cal I$-convergence.Real Anal. Exch. 26 (2000/2001), 669-686. MR 1844385 |
| Reference:
|
[9] Lorentz, G. G.: A contribution to the theory of divergent sequences.Acta Math. 80 (1948), 167-190. Zbl 0031.29501, MR 0027868, 10.1007/BF02393648 |
| Reference:
|
[10] Maddox, I. J.: A new type of convergence.Math. Proc. Camb. Philos. Soc. 83 (1978), 61-64. Zbl 0392.40001, MR 0493034, 10.1017/S0305004100054281 |
| Reference:
|
[11] Schoenberg, I. J.: The integrability of certain functions and related summability methods.Am. Math. Mon. 66 (1959), 361-375. Zbl 0089.04002, MR 0104946, 10.2307/2308747 |
| . |
