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

Year 2013, , 1 - 6, 01.04.2013
https://doi.org/10.5578/fmbd.5435

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

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.

Statistical Lacunary Summability of Sequences of Sets

Year 2013, , 1 - 6, 01.04.2013
https://doi.org/10.5578/fmbd.5435

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

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.
There are 18 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Uğur Ulusu This is me

Fatih Nuray This is me

Publication Date April 1, 2013
Submission Date August 8, 2015
Published in Issue Year 2013

Cite

APA Ulusu, U., & Nuray, F. (2013). Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14). Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 13(1), 1-6. https://doi.org/10.5578/fmbd.5435
AMA Ulusu U, Nuray F. Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14). Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2013;13(1):1-6. doi:10.5578/fmbd.5435
Chicago Ulusu, Uğur, and Fatih Nuray. “Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14)”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 13, no. 1 (April 2013): 1-6. https://doi.org/10.5578/fmbd.5435.
EndNote Ulusu U, Nuray F (April 1, 2013) Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14). Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 13 1 1–6.
IEEE U. Ulusu and F. Nuray, “Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14)”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 13, no. 1, pp. 1–6, 2013, doi: 10.5578/fmbd.5435.
ISNAD Ulusu, Uğur - Nuray, Fatih. “Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14)”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 13/1 (April 2013), 1-6. https://doi.org/10.5578/fmbd.5435.
JAMA Ulusu U, Nuray F. Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14). Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2013;13:1–6.
MLA Ulusu, Uğur and Fatih Nuray. “Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14)”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 13, no. 1, 2013, pp. 1-6, doi:10.5578/fmbd.5435.
Vancouver Ulusu U, Nuray F. Küme Dizilerinin İstatistiksel Lacunary Toplanabilirliği (011302) (9-14). Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2013;13(1):1-6.


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