Year 2019,
Volume: 7 Issue: 2, 470 - 474, 15.10.2019
Rahmet Savaş
,
Sefa Anıl Sezer
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
Rahmet Savaş
,
Sefa Anıl Sezer
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.