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Weighted Lacunary I-Statistical Convergence

Year 2017, Volume: 7 Issue: 1, 267 - 277, 31.03.2017

Abstract

In this paper, we defne the concepts of weighted lacunary -statistical convergence or S ( ) R,θ ( ) I
-convergence and[ ] R, pr ,θ I-summability, and investigate some inclusion relations

References

  • Altundağ S, Sözbir B, 2015. Weighted I-statistical convergence and its application to Korovkin type approximation theorem. International Journal of Mathematics Science and Engineering Applications, 9 (2): 63-76.
  • Başarır M, Konca Ş, 2014. On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence. Arab Journal of Mathematics and Science, 20 (2): 250-263.
  • Das P, Savaş E, Ghosal K, 2011. On generalizations of certain summability methods using ideals. Applied Mathematics Letters, 24: 1509-1514.
  • Fast H, 1951. Sur la convergence statistique. Colloquium Mathematicum, 2 (3–4): 241–244.
  • Fridy JA, Orhan C, 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160:43-51.
  • Hazarika B, Savaş E, 2011. Some I-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz function. Mathematical and Computer Modelling, 54: 2986–2998.
  • Korovkin PP, 1960. Linear Operators and Approximation Theory, Hindustan Publishing Corporation, Delhi.
  • Kostyrko P, Salat T, Wilczynski W, 2000–2001. I-convergence. Real Analysis Exchange, 26 (2): 669–686.
  • Kostyrko P, Macaj M, Salat T, Sleziak M, 2005. I-convergence and extremal I-limit points. Mathematica Slovaca, 55: 443-464.
  • Kumar S, Kumar S, Bhatia SS, 2013. On ideal version of lacunary statistical convergence of double sequences. General Mathematics Notes, 17 (1): 32-44.
  • Lahiri BK, Das P, 2005. I and I*-convergence in topological spaces, Mathematica Bohemica, 130 (2): 153-160.
  • Moricz F, Orhan C, 2004. Tauberian conditions under which statistical convergence follows from statistical summability by weighted means, Studia Scientiarum Mathematicarum Hungarica, 41: 391-403.
  • Salat T, Tripathy BC, Ziman B, 2004. On some properties of I-convergence. Tatra Mountains Mathematical Publications, 28: 279–286.
  • Schoenberg IJ, 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66: 361–375.
  • Steinhaus H, 1951. Sur la convergence ordinate et al convergence asymptotique. Colloquium Mathematicum, 2: 73–84.
  • Tripathy BC, Hazarika B, Choudhary B, 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52 (4): 473-482.

Ağırlıklı Lacunary I-İstatistiksel Yakınsaklık

Year 2017, Volume: 7 Issue: 1, 267 - 277, 31.03.2017

Abstract

Bu makalede,
S( ) R,θ ( ) I veya ağırlıklı lacunary I-istatistiksel yakınsaklık ile[ ] R pr θ I-toplanabilirlik
kavramları tanımlanmıştır ve bazı kapsama bağıntıları araştırılmıştır.



References

  • Altundağ S, Sözbir B, 2015. Weighted I-statistical convergence and its application to Korovkin type approximation theorem. International Journal of Mathematics Science and Engineering Applications, 9 (2): 63-76.
  • Başarır M, Konca Ş, 2014. On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence. Arab Journal of Mathematics and Science, 20 (2): 250-263.
  • Das P, Savaş E, Ghosal K, 2011. On generalizations of certain summability methods using ideals. Applied Mathematics Letters, 24: 1509-1514.
  • Fast H, 1951. Sur la convergence statistique. Colloquium Mathematicum, 2 (3–4): 241–244.
  • Fridy JA, Orhan C, 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160:43-51.
  • Hazarika B, Savaş E, 2011. Some I-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz function. Mathematical and Computer Modelling, 54: 2986–2998.
  • Korovkin PP, 1960. Linear Operators and Approximation Theory, Hindustan Publishing Corporation, Delhi.
  • Kostyrko P, Salat T, Wilczynski W, 2000–2001. I-convergence. Real Analysis Exchange, 26 (2): 669–686.
  • Kostyrko P, Macaj M, Salat T, Sleziak M, 2005. I-convergence and extremal I-limit points. Mathematica Slovaca, 55: 443-464.
  • Kumar S, Kumar S, Bhatia SS, 2013. On ideal version of lacunary statistical convergence of double sequences. General Mathematics Notes, 17 (1): 32-44.
  • Lahiri BK, Das P, 2005. I and I*-convergence in topological spaces, Mathematica Bohemica, 130 (2): 153-160.
  • Moricz F, Orhan C, 2004. Tauberian conditions under which statistical convergence follows from statistical summability by weighted means, Studia Scientiarum Mathematicarum Hungarica, 41: 391-403.
  • Salat T, Tripathy BC, Ziman B, 2004. On some properties of I-convergence. Tatra Mountains Mathematical Publications, 28: 279–286.
  • Schoenberg IJ, 1959. The integrability of certain functions and related summability methods. American Mathematical Monthly, 66: 361–375.
  • Steinhaus H, 1951. Sur la convergence ordinate et al convergence asymptotique. Colloquium Mathematicum, 2: 73–84.
  • Tripathy BC, Hazarika B, Choudhary B, 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52 (4): 473-482.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Şükran Konca

Submission Date April 13, 2016
Acceptance Date July 18, 2016
Publication Date March 31, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

Cite

APA Konca, Ş. (2017). Weighted Lacunary I-Statistical Convergence. Journal of the Institute of Science and Technology, 7(1), 267-277.
AMA Konca Ş. Weighted Lacunary I-Statistical Convergence. J. Inst. Sci. and Tech. March 2017;7(1):267-277.
Chicago Konca, Şükran. “Weighted Lacunary I-Statistical Convergence”. Journal of the Institute of Science and Technology 7, no. 1 (March 2017): 267-77.
EndNote Konca Ş (March 1, 2017) Weighted Lacunary I-Statistical Convergence. Journal of the Institute of Science and Technology 7 1 267–277.
IEEE Ş. Konca, “Weighted Lacunary I-Statistical Convergence”, J. Inst. Sci. and Tech., vol. 7, no. 1, pp. 267–277, 2017.
ISNAD Konca, Şükran. “Weighted Lacunary I-Statistical Convergence”. Journal of the Institute of Science and Technology 7/1 (March2017), 267-277.
JAMA Konca Ş. Weighted Lacunary I-Statistical Convergence. J. Inst. Sci. and Tech. 2017;7:267–277.
MLA Konca, Şükran. “Weighted Lacunary I-Statistical Convergence”. Journal of the Institute of Science and Technology, vol. 7, no. 1, 2017, pp. 267-7.
Vancouver Konca Ş. Weighted Lacunary I-Statistical Convergence. J. Inst. Sci. and Tech. 2017;7(1):267-7.