Keywords: sequence; statistical convergence; ${\cal I}$-convergence; almost convergence; Cesàro convergence; uniform convergence; Euler function; prime number; $\varphi $-convergence
@article{COMIM_2006_14_1_a0,
author = {Bal\'a\v{z}, V. and Strauch, O. and \v{S}al\'at, T.},
title = {Remarks on several types of convergence of bounded sequences},
journal = {Communications in Mathematics},
pages = {3--12},
year = {2006},
volume = {14},
number = {1},
mrnumber = {2298906},
zbl = {1124.40001},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a0/}
}
Baláž, V.; Strauch, O.; Šalát, T. Remarks on several types of convergence of bounded sequences. Communications in Mathematics, Tome 14 (2006) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/COMIM_2006_14_1_a0/
[1] BALÁŽ, V., ŠALÁT, T.: Uniform density $u$ and corresponding $I_u$-convergence. Math. Communication 11 (2006), 1–7.
[2] BROWN, T.C., FREEDMAN, A.R.: Arithmetic progressions in lacunary sets. Mountain J. Math. 17 (1987), 587–596. | MR
[3] BROWN, T.C., FREEDMAN, A.R.: The uniform density of sets of integers and Fermat’s Last Theorem. C. R. Math. Ref. Acad. Sci. Canada XII (1990), 1–6.. | MR
[4] BOURBAKI, N.: Éléments De Mathématique Topologie Générale Livre III. Russian translation: Obščaja topologija Osnovnye struktury, Nauka, Moskva, 1968.
[5] CONNOR, J.S.: The statistical and strong $p$-Cesàro convergence of sequences. Analysis 8 (1988), 47–63. | MR | Zbl
[6] CONNOR, J.S.: Two valued measures and summability. Analysis 10 (1990), 1–6. | MR | Zbl
[7] ERDÖS, P.: Solution of advanced problems: $\varphi $-convergence. Amer. Math. Monthly 85 (1978), 122-123.
[8] FAST, H.: Sur la convergence statistique. Coll. Math. 2 (1951), 241–244. | MR | Zbl
[9] FRIDY, J.A.: On statistical convergence. Analysis 5 (1985), 301-313. | MR | Zbl
[10] GOFFMAN, C.: Functions of finite Baire type. Amer. Math. Monthly 67 (1960), 164-165. | MR | Zbl
[11] KOLODZIEJ, W.: Selected Parts of Mathematical Analysis. PWN, Warszawa, 1970. (Polish) | MR
[12] KOSTYRKO, P., ŠALÁT, T., WILCZINSKI, W.: ${\cal I}$-convergence. Real. Anal. Exchange 26 (2000–2001), 669-686. | MR
[13] KOSTYRKO, P., MÁČAJ, M., ŠALÁT, T., SLEZIAK, M.: ${\cal I}$-convergence and extremal ${\cal I}$-limit points. Math. Slovaca 55 (2005), no. 4,, 443-464. | MR
[14] KOVÁČ, E.: On $\varphi $-convergence and $\varphi $-density. Math. Slovaca 55 (2005), no. 3, 139-150. | MR | Zbl
[15] KUIPERS, L., NIEDERREITER, H.: Uniform Distribution of Sequences. John Wiley & Sons, New York, 1974. | MR
[16] LORENTZ, G.G.: A contribution to theory of divergent sequences. Acta Math. 80 (1948), 167-190. | MR
[17] MADDOX, I.J.: A new type of convergence. Math. Proc. Cambridge Phil. Soc. 83 (1978), 61-64. | MR | Zbl
[18] MADDOX, I.J.: Steinhaus type theorems for sumability matrices. Proc. Amer. Math Soc. 45 (1974), 209-213. | MR
[19] MILLER, H.I., ORHAN, C.: On almost convergent and statistically convergent subsequences. Acta Math. Hung. 43 (2001), 135-151. | MR
[20] PETERSEN, G.: Regular Matrix Transformations. Mc-Graw Hill Publ. Comp., London-New York-Toronto-Sydney, 1966. | MR | Zbl
[21] SCHOENBERG, I.J.: The integrability of certain functions and related sumability methods. Amer. Math. Monthly 66 (1959), 361–375. | MR
[22] STRAUCH, O., PORUBSKÝ, Š.: Distribution of Sequences: A Sampler. Schriftenreihe der Slowakischen Akademie der Wissenschaften, Band 1, Peter Lang, Frankfurt am Main, 2005. | MR
[23] ŠALÁT, T.: On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139-150. | MR
[24] THOMSON, B.S. : Real Functions, . Springer-Verlag , Berlin-Göttingen-Heidelberg-New York-Tokyo, 1985. | MR | Zbl
[25] ZAJÍČEK, L.: Porosity and $\sigma $-porosity. Real. Anal. Exchange 13 (1987–88), 314-350. | MR
[26] WIERDL, M.: Almost everywhere convergence and recurrence along subsequences in ergodic theory. Ph.D. Thesis, The Ohio State University.
[27] WINKLER, R.: Hartman sets, functions and sequences - a survey. Advanced Studies in Pure Mathematics 43 (2006), 1–27. | MR