-convergence and extremal -limit points
Pavel Kostyrko; Martin Máčaj; Tibor Šalát; Martin Sleziak
Mathematica Slovaca (2005)
- Volume: 55, Issue: 4, page 443-464
- ISSN: 0139-9918
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topKostyrko, Pavel, et al. "$\mathcal {I}$-convergence and extremal $\mathcal {I}$-limit points." Mathematica Slovaca 55.4 (2005): 443-464. <http://eudml.org/doc/32332>.
@article{Kostyrko2005,
author = {Kostyrko, Pavel, Máčaj, Martin, Šalát, Tibor, Sleziak, Martin},
journal = {Mathematica Slovaca},
keywords = {density of sets; ideal of sets; porosity; - and -convergence; ; , , maximal ideal},
language = {eng},
number = {4},
pages = {443-464},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {$\mathcal \{I\}$-convergence and extremal $\mathcal \{I\}$-limit points},
url = {http://eudml.org/doc/32332},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Kostyrko, Pavel
AU - Máčaj, Martin
AU - Šalát, Tibor
AU - Sleziak, Martin
TI - $\mathcal {I}$-convergence and extremal $\mathcal {I}$-limit points
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 4
SP - 443
EP - 464
LA - eng
KW - density of sets; ideal of sets; porosity; - and -convergence; ; , , maximal ideal
UR - http://eudml.org/doc/32332
ER -
References
top- ALEXANDER R., Density and multiplicative structure of sets of integers, Acta Arith. 12 (1967), 321-332. (1967) MR0211979
- BACHRATÁ K., The maximal ideals of , Práce a Štúdie V.Š. Dopravу a Spojov v Žiline, Sér. Mat.-Fуz. 8 (1992), 5-7. (1992) MR1291582
- BROWN Т. С.-FREEDMAN A. R., The uniform density of sets of integers and Fermat's Last Theorem, С. R. Math. Acad. Sci. Soc. R. Сan. 12 (1990), 1-9. (1990) Zbl0701.11011
- BUСK R. С., The measure theoretic approach to density, Amer. J. Math. 68 (1946), 560 580. (1946) MR0018196
- BUСK R. С., Generalized asymptotic density, Amer. J. Math. 75 (1953), 335-346. (1953) MR0054000
- СARLSON S., Cauchy sequences and function rings, Amer. Math. Monthlу 88 (1981), 700-701. (1981) MR1539796
- ČERVEŇANSKÝ J., Statistical convergence and statistical continuity, Zb. Ved. Prác MtF SТU 6 (1998), 207-212. (1998)
- СONNOR J. S., The statistical and strong p-Cesàro convergence of sequences, Analуsis (Munich) 8 (1988), 47-63. (1988) MR0954458
- СONNOR J. S., Two valued measures and summability, Analуsis (Munich) 10 (1990), 373-385. (1990) MR1085803
- СONNOR J. S.-KLINE J., On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl. 197 (1996), 392-399. (197) MR1372186
- FASТ H., Sur la convergence statistique, Соllоq. Math. 2 (1951), 241-244. (1951) MR0048548
- FREEDMAN A. R.-SEMBER J. J., Densities and summability, Pacific J. Math. 95 (1981), 293-305. (1981) Zbl0504.40002MR0632187
- FRIDY J. A., On statistical convergence, Analуsis (Munich) 5 (1985), 301-313. (1985) Zbl0588.40001
- FRIDY J. A., Statistical limit points, Prоc. Amer. Math. Sоc. 118 (1993), 1187-1192. (1993) Zbl0776.40001MR1181163
- FRIDY J. A.-ORHAN, С, Statistical limit superior and limit inferior, Prоc. Amer. Math.Sоc. 125 (1997), 3625-3631. (1997) Zbl0883.40003MR1416085
- GILLMAN L.-JERISON M., Rings of Continuous Functions, Van Nоstrand, Princetоn, 1950. (1950) MR0116199
- KOSТYRKO P.-MAČAJ M.-ŠALÁТ Т.-SТRAUСH O., On statistical limit points, Prоc. Amer. Math. Sоc. 129 (2001), 2647-2654.
- KOSТYRKO P.-ŠALÁТ Т.-WILСZYŃSKI W., -convergence, Real Anal. Exchange 26 (2000-2001), 669-686.
- KURAТOWSKI С., Topologie I, PWN, Warszawa, 1958. (1958)
- MAHARAM D., Finitely additive measures on the integers, Sankhуä Ser. A 38 (1976), 44-54. (1976) Zbl0383.60008MR0473132
- MAČAJ M.-MIŠÍK L.-ŠALÁТ Т.-ТOMANOVÁ J., On a class of densities of sets of positive integers, Acta Math. Univ. Соmenian. (N.S.) 72 (2003), 213-221. Zbl1087.11006MR2040266
- MAZUR K., -ideals and and -gaps in the Boolean algebras , Fund. Math. 138 (1991), 103-111. (1991) MR1124539
- MIKUSIŃSKI P., Axiomatic theory of convergence, Pr. Nauk. Uniw. ŚI. Katow. 12 (1982), 13-21. (Polish) (1982) Zbl0508.40003MR0663359
- MILLER H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811-1819. (1995) Zbl0830.40002MR1260176
- NAGATA J., Modern General Topology, Noth-Holland Publ. Comp., Amsterdam-London, 1974. (1974) MR0474164
- NEUBRUN T.-SMÍTAL J.-ŠALÁT T., On the structure of the space , Rev. Roumaine Math. Pures Appl. 13 (1968), 377-386. (1968) MR0234275
- NURAY F.-RUCKLE W. H., Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513-527. Zbl0955.40001MR1758553
- OLEVSKII V., A note on the Banach-Steinhaus theorem, Real Anal. Exchange 17 (1991-1992), 399-401. (1991) MR1147379
- OSTMANN H. H., Additive Zahlentheorie I, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1956. (1956) Zbl0072.03101MR0098721
- PETERSEN G. M., Regular Matrix Transformations, Mc Graw-Hill, London-New York-Toronto-Sydney, 1966. (1966) Zbl0159.35401MR0225045
- POWELL B. J.-ŠALÁT T., Convergene of subseries of the harmonic series and asymptotic densities of sets of positive integers, Publ. Inst. Math. (Beograd) (N.S.) 50(64) (1991), 60-70. (1991) MR1252159
- ŠALÁT T., On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150. (1980) Zbl0437.40003MR0587239
- ŠALÁT T.-TIJDEMAN R., Asymptotic densities of sets of positive integers, Math. Slovaca 33 (1983), 199-207. (1983) Zbl0516.10052MR0699090
- ŠALÁT T.-TIJDEMAN R., On density measures of sets of positive integers, In: Topics in Classical Number Theory. Colloq. Math. Soc. Janos Bolyai 34, Budapest, 1981, pp. 1445-1457. (1981) MR0781191
- ŠALÁT T.-TOMANOVA J., On the product of divisors of a positive integer, Math. Slovaca 52 (2002), 271-287. Zbl1005.11002MR1936333
- SCHINZEL A.-ŠALÁT T., Remarks on maximum and minimum exponents in factoring, Math. Slovaca 44 (1994), 505-514. (1994) Zbl0821.11004MR1338424
- SCHOENBERG I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375. (1959) Zbl0089.04002MR0104946
- THOMSON B. S., Real Functions, Springer-Verlag, Berlin-Gottingen-Heidelberg-New York-Tokyo, 1985. (1985) Zbl0581.26001MR0818744
- ZAJÍČEK L., Porosity and -porosity, Real Anal. Exchange 13 (1987-88), 314-350. (1987) Zbl0666.26003MR0943561
Citations in EuDML Documents
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- Mehmet Özarslan, I-convergence theorems for a class of k-positive linear operators
- Ladislav Matejíčka, Some remarks on -faster convergent infinite series
- Antonio Boccuto, Xenofon Dimitriou, Nikolaos Papanastassiou, Ideal convergence and divergence of nets in -groups
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