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Porosity Supremum-Infimum and Porosity Convergence

Year 2018, Volume: 6 Issue: 1, 163 - 170, 15.04.2018

Abstract

In this paper, by using porosity notion for subsets of natural numbers at infinity porosity lower and porosity upper bound of real valued sequences will be defined. By using these new notions, definitions of porosity infimum and porosity supremum will be given, respectively. For a given sequence, the equivalence of porosity infimum and porosity supremum is necessary and sufficient condition for to existence of porosity convergence but it is necessary, not sufficient, condition for to existence of usual convergence.

References

  • [1] Altınok, M., Dovgoshey, O. and K¨uc¸ ¨ukaslan, M., Local one-sided porosity and pretangent spaces, Analysis, Vol:36, No.3, (2016), 147-171.
  • [2] Altınok, M. and Küçükaslan, M., On porosity-convergence of real valued sequences, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.), Accepted 2016.
  • [3] Altınok, M. and Küçükaslan, M., Porosity Limit and Cluster Points of Real Valued Sequences, To appeared.
  • [4] Denjoy, A., Sur une propri ´ et ´ e des s ´ eries trigonom ´ etriques, Verlag v.d. G. V. der Wie-en Natuur. Afd., Vol:29, (1920), 220-232.
  • [5] Dolˇzenko, E. P., Boundary properties of arbitrary functions, (Russian), Izv. Akad. Nauk SSSR Ser. Math., Vol:31, (1967), 3-14.
  • [6] Kaya, E., Küçükaslan, M. and Wagner R., On Statistical Convergence and Statistical Monotonicity, Annales Univ. Sci. Budapest. Sect. Comp., Vol:39, (2013), 257-270.
  • [7] Khintchine, A., An investigation of the structure of measurable functions, (Russian), Mat. Sbornik, Vol:31, (1924), 265-285.
  • [8] Küçükaslan, M. and Altınok, M., Statistical supremum-infimum and statistical convergence, The Aligarh Bulletin of Mathematics, Vol:32 No.1-2, (2013), 39-54.
  • [9] Thomson, B. S., Real Functions, Lecture Notes in Mathematics, 1170, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985.
Year 2018, Volume: 6 Issue: 1, 163 - 170, 15.04.2018

Abstract

References

  • [1] Altınok, M., Dovgoshey, O. and K¨uc¸ ¨ukaslan, M., Local one-sided porosity and pretangent spaces, Analysis, Vol:36, No.3, (2016), 147-171.
  • [2] Altınok, M. and Küçükaslan, M., On porosity-convergence of real valued sequences, An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.), Accepted 2016.
  • [3] Altınok, M. and Küçükaslan, M., Porosity Limit and Cluster Points of Real Valued Sequences, To appeared.
  • [4] Denjoy, A., Sur une propri ´ et ´ e des s ´ eries trigonom ´ etriques, Verlag v.d. G. V. der Wie-en Natuur. Afd., Vol:29, (1920), 220-232.
  • [5] Dolˇzenko, E. P., Boundary properties of arbitrary functions, (Russian), Izv. Akad. Nauk SSSR Ser. Math., Vol:31, (1967), 3-14.
  • [6] Kaya, E., Küçükaslan, M. and Wagner R., On Statistical Convergence and Statistical Monotonicity, Annales Univ. Sci. Budapest. Sect. Comp., Vol:39, (2013), 257-270.
  • [7] Khintchine, A., An investigation of the structure of measurable functions, (Russian), Mat. Sbornik, Vol:31, (1924), 265-285.
  • [8] Küçükaslan, M. and Altınok, M., Statistical supremum-infimum and statistical convergence, The Aligarh Bulletin of Mathematics, Vol:32 No.1-2, (2013), 39-54.
  • [9] Thomson, B. S., Real Functions, Lecture Notes in Mathematics, 1170, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Maya Altınok 0000-0002-6671-743X

Publication Date April 15, 2018
Submission Date May 24, 2017
Acceptance Date December 12, 2017
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Altınok, M. (2018). Porosity Supremum-Infimum and Porosity Convergence. Konuralp Journal of Mathematics, 6(1), 163-170.
AMA Altınok M. Porosity Supremum-Infimum and Porosity Convergence. Konuralp J. Math. April 2018;6(1):163-170.
Chicago Altınok, Maya. “Porosity Supremum-Infimum and Porosity Convergence”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 163-70.
EndNote Altınok M (April 1, 2018) Porosity Supremum-Infimum and Porosity Convergence. Konuralp Journal of Mathematics 6 1 163–170.
IEEE M. Altınok, “Porosity Supremum-Infimum and Porosity Convergence”, Konuralp J. Math., vol. 6, no. 1, pp. 163–170, 2018.
ISNAD Altınok, Maya. “Porosity Supremum-Infimum and Porosity Convergence”. Konuralp Journal of Mathematics 6/1 (April 2018), 163-170.
JAMA Altınok M. Porosity Supremum-Infimum and Porosity Convergence. Konuralp J. Math. 2018;6:163–170.
MLA Altınok, Maya. “Porosity Supremum-Infimum and Porosity Convergence”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 163-70.
Vancouver Altınok M. Porosity Supremum-Infimum and Porosity Convergence. Konuralp J. Math. 2018;6(1):163-70.
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