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Year 2019, Volume: 7 Issue: 2, 470 - 474, 15.10.2019

Abstract

References

  • [1] R. Colak, Statistical convergence of order a, Modern Methods in Analysis and its Applications, Anamaya Pub., New Delhi, (2010), 121–129.
  • [2] P. Das, E. Savas and S. K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Lett. 24 (2011), 1509–1514.
  • [3] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [4] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
  • [5] J. A. Fridy and C. Orhan, Lacunary statistical convergence. Pac. J. Math. 160 (1993), 43–51.
  • [6] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange 26 (2000/01), 669–685.
  • [7] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I–Convergence and extremal I–Limit points, Math. Slovaca, 55 (2005), 443—464.
  • [8] M. S. Marouf, Asymptotic equivalence and summability, Internat. J. Math. Math. Sci. 16 (1993), 755–762.
  • [9] R. F. Patterson, On asymptotically statistical equivalent sequences, Demonstratio Math. 36 (2003), 149–153.
  • [10] E. Savas, On I-Asymptotically lacunary statistical equivalent sequences, Adv. Difference Equ. 2013:111 (2013), 7 p.
  • [11] E. Savas, On asymptotically I-Lacunary statistical equivalent sequences of order a, The International Conference on Pure Mathematics-Applied Mathematics Venice, Italy, (2014).
  • [12] E. Savas, Generalized summability methods of functions using ideals, AIP Conference Proceedings V. 1676, (2015).
  • [13] E. Savas, On generalized statistically convergent functions via ideals, Appl. Math. 10 (2016), 943–947.
  • [14] E. Savas, Asymptotically I-Lacunary statistical equivalent of order a for sequences of sets, J. Nonlinear Sci. Appl. 10 (2017), 2860–2867.
  • [15] E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), 826–830.
  • [16] E. Savas, P. Das and S. Dutta, A note on strong matrix summability via ideals, Appl. Math. Lett., 25 (2012), 733–738.
  • [17] E. Savas and H. Gumus, A generalization on I–asymptotically lacunary statistical equivalent sequences, J. Inequal. Appl., 2013:270 (2013), 9 p.
  • [18] I.J.Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959) 361–375.
  • [19] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.
  • [20] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.

On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$

Year 2019, Volume: 7 Issue: 2, 470 - 474, 15.10.2019

Abstract

The aim of this paper is to provide a new approach to some well known summability methods. We first define  asymptotically ${\rm I}$-statistical equivalent functions of order $\alpha $, asymptotically ${\rm I} _{\theta} $-statistical equivalent functions of order $\alpha$ and strongly ${\rm I}$-lacunary equivalent functions of order $\alpha$ by taking two nonnegative real-valued Lebesgue measurable functions $x(t)$ and $y(t)$ in the interval $(1,\infty)$ instead of sequences and later we investigate their relationship.

References

  • [1] R. Colak, Statistical convergence of order a, Modern Methods in Analysis and its Applications, Anamaya Pub., New Delhi, (2010), 121–129.
  • [2] P. Das, E. Savas and S. K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Lett. 24 (2011), 1509–1514.
  • [3] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
  • [4] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313.
  • [5] J. A. Fridy and C. Orhan, Lacunary statistical convergence. Pac. J. Math. 160 (1993), 43–51.
  • [6] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange 26 (2000/01), 669–685.
  • [7] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I–Convergence and extremal I–Limit points, Math. Slovaca, 55 (2005), 443—464.
  • [8] M. S. Marouf, Asymptotic equivalence and summability, Internat. J. Math. Math. Sci. 16 (1993), 755–762.
  • [9] R. F. Patterson, On asymptotically statistical equivalent sequences, Demonstratio Math. 36 (2003), 149–153.
  • [10] E. Savas, On I-Asymptotically lacunary statistical equivalent sequences, Adv. Difference Equ. 2013:111 (2013), 7 p.
  • [11] E. Savas, On asymptotically I-Lacunary statistical equivalent sequences of order a, The International Conference on Pure Mathematics-Applied Mathematics Venice, Italy, (2014).
  • [12] E. Savas, Generalized summability methods of functions using ideals, AIP Conference Proceedings V. 1676, (2015).
  • [13] E. Savas, On generalized statistically convergent functions via ideals, Appl. Math. 10 (2016), 943–947.
  • [14] E. Savas, Asymptotically I-Lacunary statistical equivalent of order a for sequences of sets, J. Nonlinear Sci. Appl. 10 (2017), 2860–2867.
  • [15] E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), 826–830.
  • [16] E. Savas, P. Das and S. Dutta, A note on strong matrix summability via ideals, Appl. Math. Lett., 25 (2012), 733–738.
  • [17] E. Savas and H. Gumus, A generalization on I–asymptotically lacunary statistical equivalent sequences, J. Inequal. Appl., 2013:270 (2013), 9 p.
  • [18] I.J.Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959) 361–375.
  • [19] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.
  • [20] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Rahmet Savaş

Sefa Anıl Sezer

Publication Date October 15, 2019
Submission Date September 2, 2019
Acceptance Date September 28, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Savaş, R., & Sezer, S. A. (2019). On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$. Konuralp Journal of Mathematics, 7(2), 470-474.
AMA Savaş R, Sezer SA. On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$. Konuralp J. Math. October 2019;7(2):470-474.
Chicago Savaş, Rahmet, and Sefa Anıl Sezer. “On Asymptotically I-Lacunary Statistical Equivalent Functions of Order $\alpha$”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 470-74.
EndNote Savaş R, Sezer SA (October 1, 2019) On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$. Konuralp Journal of Mathematics 7 2 470–474.
IEEE R. Savaş and S. A. Sezer, “On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$”, Konuralp J. Math., vol. 7, no. 2, pp. 470–474, 2019.
ISNAD Savaş, Rahmet - Sezer, Sefa Anıl. “On Asymptotically I-Lacunary Statistical Equivalent Functions of Order $\alpha$”. Konuralp Journal of Mathematics 7/2 (October 2019), 470-474.
JAMA Savaş R, Sezer SA. On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$. Konuralp J. Math. 2019;7:470–474.
MLA Savaş, Rahmet and Sefa Anıl Sezer. “On Asymptotically I-Lacunary Statistical Equivalent Functions of Order $\alpha$”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 470-4.
Vancouver Savaş R, Sezer SA. On Asymptotically I-lacunary Statistical Equivalent Functions of Order $\alpha$. Konuralp J. Math. 2019;7(2):470-4.
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