Lacunary A- Convergence

ISSN: 2146-4987
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2011
Yayıncı: ZONGULDAK BÜLENT ECEVİT ÜNİVERSİTESİ

In this paper we introduce the concept of LacunarySummability. We also give the relations between these summability and Lacunary statistical Summability. Following the concept of statistical limit superior and inferior, we give a definition of Lacunary limit superior and inferior which yields natural relationships among these ideas: x is Lacunary convergent if and only if Lacunary core of is also introduced and it is proved that a bounded sequence that summable to its Lacunary limit superior is Lacunary convergent.

Keywords:

Lacunary Convergence, Lacunary A-Summability, Lacunary A-convergence Lacunary A-core.,

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Aktuğlu, H., Gezer H. 2009. Lacunary equi-statistical convergence of positive linear operators, Cent. Eur. J. Math., 558-567.
Connor, J. 1988. The statictical and strong p Cesaro convergence of sequences. Analysis, 47-63.
Connor, JS., Kline, J. 1996. On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl., 197:392-399.
Duman, O., Khan, MK., Orhan, C. 2003. A-statistical convergence of approximation operators. Math. Inequal. Appl., 689-699.
Freedman, AR., Sember, JJ. 1981. Density and summability. Pac. J. Math, 95: 293-305.
Fridy, JA. 1953. Generalized asymtotic density. Am. J. Math. 75:335-346.
Fridy, JA. 1978. Minimal rates of summability, Can. J. Math., 30: 808-816.
Fridy, J., Miller, HI. 1991. A matrix characterization of statistical convergence. Analysis 11: 59-66.
Fridy, JA., Orhan, C. 1993. Lacunary statistical convergence. Pac. J. Math.,160:43-51.
Fridy, JA., Orhan, C. 1996. Statical limit superior and limit inferior. Proc. Amer. Math. Soc.,125 (12): 3625-3631.
Mursaleen M., Osama H., Edely, H. 2004. Generalised statistical convergence. Inform. Sci., 287-294.
Mursaleen M., Osama H., Edely, H. 2009. On statistical A-summability. Math. Comput. Model., 672-680.