Statistical limit superior and limit inferior

Proceedings of the American Mathematical Society

Volumn 125, Issue 12, 1997, Pages 3625-3631

  Fridy, J A ^a   Orhan, C ^b  

^a KENT STATE UNIVERSITY   (United States)

^b ANKARA UNIVERSITY   (Turkey)

Author keywords

Core of a sequence; Natural density; Statistical cluster point; Statistically convergent sequence

Indexed keywords

EID: 21944449161     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-04000-8     Document Type: Article

References (19)

1. R. C. Buck, Generalized asymptotic density, Amer. J. Math. 75(1953), 335-346. MR 14:854f
2. J. S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis 8(1988), 47-63. MR 89k:40013
3. J. S. Connor and M. A. Swardson, Strong integral summability and the Stone-Cech compactification of the half-line, Pacific J. Math. 157 (1993), 201-224. MR 94f:40007
4. J.S. Connor and M.A. Swardson, Measures and ideals of C*(X), Annals N.Y. Acad.Sci. 104 (1994), 80-91. MR 95b:54022
5. J.S. Connor and J. Kline, On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl. 197 (1996), 392-399. MR 96m:40001
6. P. Erdös and G. Tenenbaum, Sur les densities de certaines suites d'entries, Proc. London Math. Soc. 59 (1989), 417-438. MR 90h:11087
7. H. Fast, Sur la convergence statistique, Colloq. Math. 2(1951), 241-244. MR 14:29c
8. J.A. Fridy, On statistical convergence, Analysis 5(1985), 301-313. MR 87b:40001
9. _, Statistical limit points, Proc. Amer. Math. Soc. 118(1993), 1187-1192. MR 94e:40008
10. J. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl. 173 (1993), 497-504. MR 95f:40004
11. J. Fridy and H.I. Miller, A matrix characterization of statistical convergence, Analysis 11 (1991), 59-66. MR 92e:40001
12. G.H. Hardy, Divergent Series, Oxford Univ. Press, London, 1949. MR 11:25a
13. K. Knopp, Zur Theorie der Limitierungsverfahren(Erste Mitteilung), Math. Zeit. 31(1930), 115-127.
14. I.J. Maddox, Steinhaus type theorems for summability matrices, Proc. Amer. Math. Soc. 45(1974), 209-213. MR 51:1192
15. _, Some analogues of Knopp's Core Theorem, Internat. J. Math. & Math. Sci., 2(1979), 605-614, MR 81m:40012
16. _, Statistical convergence in locally convex spaces, Math. Cambridge Phil. Soc. 104 (1988), 141-145. MR 89k:40012
17. H.I. Miller, A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811-1819. MR 95h:40010
18. I. Niven, H.S. Zuckerman, and H. Montgomery, An Introduction to the Theory of Numbers, Fifth Ed., Wiley, New York, 1991. MR 911:11001
19. A. Zygmund, Trigonometric Series, 2nd Ed., Cambridge Univ. Press, 1979. MR 58:29731