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ON STATISTICALLY CONVERGENT IN FINITE DIMENSIONAL SPACES

Year 2008, Volume: 3 Issue: 1, 113 - 122, 01.06.2008

Abstract

Abstract: In this paper, the notion of statistical convergence, which was introduced by
Steinhaus (1951), was studied in Rm ; and some concepts and theorems, whose
statistical correspondence for the real number sequences were given, were carried to
Rm . In addition, the concepts of the statistical limit point and the statistical cluster point
were given and it was mentioned that these two concepts were'nt equal in Fridy's study
in 1993. These concepts were given in Rm and the inclusion correlation between these
concepts was studied.
Key words: Statistical convergence, statistical boundedness, statistically Cauchy
sequence, statistical limit point, statistical cluster point.
Mathematics Subject Classifications (2000): 40A05
SONLU BOYUTLU UZAYLARDA İSTATİSTİKSEL YAKINSAKLIK
ÜZERİNE
Özet: Bu makalede Steinhaus (1951) tarafından verilen istatistiksel yakınsaklık kavramı
Rm de incelenip, reel sayı dizileri için istatistiksel benzerleri verilen bazı kavram ve
teoremler R m e taşınmıştır. 1993'de Fridy tarafından yapılan çalışmada istatistiksel
limit noktası ve istatistiksel yığılma noktası kavramları verilip bu iki kavramın birbirine
denk olmadığından bahsedilmiştir. Bu kavramlar R m de verilip aralarındaki kapsama
bağıntısı incelenmiştir.
Anahtar kelimeler: İstatistiksel Yakınsaklık, İstatistiksel Sınırlılık, İstatistiksel Cauchy
Dizisi, İstatistiksel Limit Noktası, İstatistiksel Yığılma Noktası.

References

  • BUCK RC, 1953. Generalized asymptotic density, American Journal of Mathematics, 75, 335-346.
  • CONNOR JS, 1985. Some applications of functional analysis to summability theory, Ph.D thesis, Kent State University.
  • CONNOR JS, 1988. The statistical and strong P-Cesáro convergence of sequences, Analysis, 8, 47-63.
  • FAST H, 1951. Sur la convergence statistique, Collog. Math, 2, 241-244.
  • FRIDY JA, 1985. On statistical convergence, Analysis, 5, 301-313.
  • FRIDY JA, 1993. Statistical limit point,Proceedings of the American Mathematical Society, 4, 1187-1192.
  • MADDOX IJ 1988. Statistical convergence in a locally convex sequence space, Math. Proc. Camp. Phil. Soc., 104, 141-145.
  • PEHLIVAN S, MAMEDOV M, 2000. Statistical cluster point and turnpike, Optimization, 48, 93-106.
  • RATH D, TRIPATHY BC, 1994. On statistically convergent and statistically Cauchy sequences, Indian Journal of Pure and Applied Mathematics, 25, 381-386.
  • SALAT T, 1980. On Statistically convergent sequences of real numbers, Mathematica. Slovaca, 30, 139-150.
  • SCHOENBERG IJ, 1959. The integrability of certain functions and related summability methods, American. Mathematical. Monthly, 66, 361-375.
  • STEINHAUS H, 1951. Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math, 2, 73-74.
Year 2008, Volume: 3 Issue: 1, 113 - 122, 01.06.2008

Abstract

References

  • BUCK RC, 1953. Generalized asymptotic density, American Journal of Mathematics, 75, 335-346.
  • CONNOR JS, 1985. Some applications of functional analysis to summability theory, Ph.D thesis, Kent State University.
  • CONNOR JS, 1988. The statistical and strong P-Cesáro convergence of sequences, Analysis, 8, 47-63.
  • FAST H, 1951. Sur la convergence statistique, Collog. Math, 2, 241-244.
  • FRIDY JA, 1985. On statistical convergence, Analysis, 5, 301-313.
  • FRIDY JA, 1993. Statistical limit point,Proceedings of the American Mathematical Society, 4, 1187-1192.
  • MADDOX IJ 1988. Statistical convergence in a locally convex sequence space, Math. Proc. Camp. Phil. Soc., 104, 141-145.
  • PEHLIVAN S, MAMEDOV M, 2000. Statistical cluster point and turnpike, Optimization, 48, 93-106.
  • RATH D, TRIPATHY BC, 1994. On statistically convergent and statistically Cauchy sequences, Indian Journal of Pure and Applied Mathematics, 25, 381-386.
  • SALAT T, 1980. On Statistically convergent sequences of real numbers, Mathematica. Slovaca, 30, 139-150.
  • SCHOENBERG IJ, 1959. The integrability of certain functions and related summability methods, American. Mathematical. Monthly, 66, 361-375.
  • STEINHAUS H, 1951. Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math, 2, 73-74.
There are 12 citations in total.

Details

Primary Language English
Journal Section Makaleler
Authors

Ayşe Nur Güncan This is me

Publication Date June 1, 2008
Published in Issue Year 2008 Volume: 3 Issue: 1

Cite

IEEE A. N. Güncan, “ON STATISTICALLY CONVERGENT IN FINITE DIMENSIONAL SPACES”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 3, no. 1, pp. 113–122, 2008, doi: 10.29233/sdufeffd.134646.