Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14)

Year 2013, Volume: 13 Issue: 1, 1 - 6, 01.04.2013

Uğur Ulusu Fatih Nuray

https://doi.org/10.5578/fmbd.5435

Cited By: 2

Abstract

Bu çalışmada, küme dizileri için Wijsman istatistiksel lacunary toplanabilme kavramı tanımlandı ve bu kavramın daha önceden Ulusu ve Nuray (2012) tarafından verilen küme dizilerinin Wijsman lacunary istatistiksel yakınsaklık kavramı ile ilişkisinden bahsedildi. Ayrıca, bir küme dizisinin Wijsman istatistiksel lacunary toplanabilmesi ve Wijsman lacunary istatistiksel yakınsak olabilmesi için gerek ve yeter şartlar verildi

Keywords

İstatistiksel yakınsaklık; Lacunary istatistiksel yakınsaklık; İstatistiksel lacunary toplanabilme; küme dizisi; Wijsman yakınsaklık

Statistical Lacunary Summability of Sequences of Sets

Abstract

In this paper, we define Wijsman statistical lacunary summability for sequences of sets and establish the relationship between Wijsman lacunary statistical convergence which was previously given by Ulusu and Nuray (2012). Also, necessary and sufficient conditions for Wijsman statistical lacunary summability and Wijsman lacunary statistical convergence of a sequence of sets is given

Keywords

Statistical convergence; Lacunary statistical convergence; Statistical lacunary summability; Sequence of sets; Wijsman convergence

References

• Aubin, J.-P. and Frankowska, H., 1990. Set-valued analysis. Birkhauser, Boston.
• Baronti, M. and Papini, P., 1986. Convergence of sequences of sets. In: Micchelli, C.A., Pai, D.V., Methods of functional analysis in approximation theory. ISNM 76, Birkhauser-Verlag, Basel, 133-155.
• Beer, G., 1985. On convergence of closed sets in a metric space and distance functions. Bulletin of the Australian Mathematical Society, 31, 421-432.
• Beer, G., 1994. Wijsman convergence: A survey. Set- Valued and Variational Analysis, 2, 77-94.
• Buck, R. C., 1953. Generalized asymptotic density. American Journal of Mathematics, 75, 335-346.
• Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241-244.
• Fridy, J.A., 1985. On statistical convergence. Analysis, 5, 301-313.
• Fridy, J.A. and Orhan, C., 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160, 43-51.
• Maddox, I. J., 1978. A new type of convergence. Mathematical Proceedings of the Cambridge Philosophical Society, 83, 61-64.
• Mursaleen, M. and Alotaibi, A., 2011. Statistical lacunary summability and a Korovkin type approximation theorem. Annali dell’Universitadi Ferrara, 57, 373- 381.
• Nuray, F. and Rhoades, B.E., 2012. Statistical convergence of sequences of sets. Mathematici, 49, 87-99. Fasciculi
• Powel, R. E. and Shah, S. M., 1972. Summability theory and its applications. Van Nostrand-Rheinhold, London.
• Salat, T., 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca, 30, 139-150.
• Sonntag, Y. and Zalinescu, C., 1993. Set convergences. An attempt of classification. Transactions of the American Mathematical Society, 340, 199-226.
• Ulusu, U. and Nuray, F., 2012. Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics, 4(2), 99-109.
• Ulusu, U., 2013. Küme dizilerinin lacunary istatistiksel yakınsaklığı, Üniversitesi Fen Bilimleri Enstitüsü, Afyonkarahisar, 75 sayfa. tezi, Afyon Kocatepe
• Wijsman, R.A., 1964. Convergence of sequences of convex sets, cones and functions. American Mathematical Society. Bulletin, 70, 186-188.
• Wijsman, R. A., 1966. Convergence of sequences of convex sets, cones and functions II. Transactions of the American Mathematical Society, 123(1), 32-45.