You are here

Home » Content

On Statistical Boundedness of Metric Valued Sequences

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2012

Key Words:

Author NameUniversity of AuthorFaculty of Author

AMS Codes:

Abstract (2. Language): 
In this work, statistical boundedness is defined in ametric space and, statistical boundedness of metric valued sequences and their subsequences are studied. The interplay between the statistical boundedness and boundedness in a metric spaces are also studied, and it is shown that boundedness imply statistical boundedness and if the number of elements of the metric space is finite then these two concepts coincide. Moreover, here is given analogy of Balzano-Weierstrass Theorem.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon arastirmax-statistical-boundedness-metric-valued-sequences.pdf
  • 2
174-186
  • English

REFERENCES

References: 

[1] F Abdullayev, O Dovgoshey and M Küçükaslan. Metric spaces with unique pretangent
spaces. Conditions of the uniqueness, Ann. Acad. Sci. Fenn. Math., 36: 353-392, 2011.
[2] J Cervanansky. Statistical covergence and statistical continuity. Zbornik vedeckych prac
MtF STU. 6: 924–931, 1943.
[3] J Connor. The statistical and strong p-Cesaro convergence of sequences. Analysis, 8:207–
212, 1998.
[4] O Dovgoshey. Tangent spaces to metric spaces and to their subspaces. Ukr. Mat. Visn.,
5:468–485, 2008.
[5] O Dovgoshey, F Abdullayev and M Küçükaslan. Compactness and boundedness of tangent
spaces to metric spaces. Beiträge Algebra Geom., 51:547–576, 2010.
[6] O Dovgoshey and O Martio. Tangent spaces to Metric spaces. Reports in Math. Helsinki
Univ., 480: 2008.
[7] H Fast. Sur la convergence statistique, Colloquium Mathematicum, 2:241–244, 1951.
[8] J Fridy. On statistical convergence. Analysis, 5:301–313, 1995.
[9] J Fridy and M Khan. Tauberian theorems via statistical convergence. J. Math. Anal. Appl.,
228:73–95, 1998.
[10] J Fridy and H Miller. A Matrix characterization of statistical convergence. Analysis,
11:59–66, 1991.
[11] J Heinonen. Lectures on Analysis on Metric Spaces. Springer, 2001.
[12] M Küçükaslan, U De˘ger and O Dovgoshey. On Statistical Convergence of Metric Valued
Sequences. arXiv:1203.2584v1 [math.FA], 2011.
[13] M Maˇcaj and T Šalát. Statistical convergence of subsequence of a given sequence. Mathematica
Bohemica, 126:191–208, 2001.
[14] H Miller. A measure theoretical subsequence characterization of statistical convergence.
Transactions of the AMS, 347:1811–1819, 1995.
[15] T Šalát. On statistically convergent sequences of real numbers. Math. Slovaca, 30:139–
150, 1980.
[16] A Zygmund. Trigonometric Series. Cambridge University Press, Cambridge, UK, 1979.

Thank you for copying data from http://www.arastirmax.com