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## Open Mathematics

2006 | 4 | 4 | 648-655
Tytuł artykułu

### σ-asymptotically lacunary statistical equivalent sequences

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every ε > 0 $$\mathop {\lim }\limits_r \frac{1}{{h_r }}\left\{ {k \in I_r :\left| {\frac{{x_{\sigma ^k (m)} }}{{y_{\sigma ^k (m)} }} - L} \right| \geqslant \in } \right\} = 0$$ uniformly in m = 1, 2, 3, ..., (denoted by x $$\mathop \sim \limits^{S_{\sigma ,\theta } }$$ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically equivalent analogues of Fridy and Orhan’s theorems in  and analogues results of Das and Patel in  shall also be presented.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
648-655
Opis fizyczny
Daty
wydano
2006-12-01
online
2006-12-01
Twórcy
autor
• Yüzüncü Yil University
autor
• University of North Florida
Bibliografia
•  G. Das and B.K. Patel: “Lacunary distribution of sequences”, Indian J. Pure Appl. Math., Vol. 26(1), (1989), pp. 54–74.
•  H. Fast: “Sur la convergence statistique”, Collog. Math., Vol. 2, (1951), pp. 241–244.
•  J.A. Fridy: “Minimal rates of summability”, Can. J. Math., Vol. 30(4), (1978), pp. 808–816.
•  J.A. Fridy: “On statistical sonvergence”, Analysis, Vol. 5, (1985), pp. 301–313.
•  J.A. Fridy and C. Orhan: “Lacunary statistical sonvergent”, Pacific J. Math., Vol. 160(1), (1993), pp. 43–51.
•  G.G. Lorentz: “A contribution to the theory of divergent sequences”, Acta. Math., Vol. 80, (1948), pp. 167–190. http://dx.doi.org/10.1007/BF02393648
•  Mursaleen: “Some new spaces of lacunary sequences and invariant means”, Ital. J. Pure Appl. Math., Vol. 11, (2002), pp. 175–181.
•  Mursaleen: “New invariant matrix methods of summability”, Quart. J. Math. Oxford, Vol. 34(2), (1983), pp. 133, 77–86.
•  M. Marouf: “Asymptotic equivalence and summability”, Int. J. Math. Math. Sci., Vol. 16(4), (1993), pp. 755–762. http://dx.doi.org/10.1155/S0161171293000948
•  R.F. Patterson: “On asymptotically statistically equivalent sequences”, Demonstratio Math., Vol. 36(1), (2003), pp. 149–153.
•  R.F. Patterson and E. Savaş: “On asymptotically lacunary statistically equivalent sequences”, (in press).
•  P. Schaefer: “Infinite matrices and invariant means”, Proc. Amer. Math. Soc., Vol. 36, (1972), pp. 104–110. http://dx.doi.org/10.2307/2039044
Typ dokumentu
Bibliografia
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