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Year 2019, Volume: 2 Issue: 3, 189 - 193, 30.12.2019

Mikail Et , Muhammed Cinar , Hacer Şengül

Abstract

References

  • [1] A. Zygmund, Trigonometric series, Cambridge University Press, Cambridge, London and New York, 1979.
  • [2] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73–74.
  • [3] H. Fast, Sur la convergence statistique, Colloq. Math.,2 (1951), 241–244.
  • [4] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [5] S. Gupta, V. K. Bhardwaj, On deferred f-statistical convergence, Kyungpook Math. J. 58(1) (2018), 91–103.
  • [6] N. L. Braha, H. M. Srivastava, S. A. Mohiuddine, A Korovkin’s type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean, Appl. Math. Comput., 228 (2014), 162–169.
  • [7] M. Çınar, M. Karaka¸s, M. Et, On pointwise and uniform statistical convergence of order $\alpha$ for sequences of functions, Fixed Point Theory Appl. 33(2013), 11.
  • [8] J. S. Connor, The Statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988), 47–63.
  • [9] M. Et, A. Alotaibi, S. A. Mohiuddine, On $(\Delta^{m},I)-$-statistical convergence of order $\alpha$; The Scientific World Journal, 2014, 535419 DOI: 10.1155/2014/535419.
  • [10] M. Et, S. A. Mohiuddine, A. Alotaibi, On $\lambda $-statistical convergence and strongly $\lambda -$summable functions of order $\alpha$, J. Inequal. Appl. 469 (2013), 8.
  • [11] M. Et, B. C. Tripathy, A. J. Dutta, On pointwise statistical convergence of order $\alpha$ of sequences of fuzzy mappings, Kuwait J. Sci. 41(3) (2014), 17–30.
  • [12] M. Et, R. Colak, Y. Altın, Strongly almost summable sequences of order $\alpha$; Kuwait J. Sci. 41(2), (2014), 35–47.
  • [13] E. Savaş, M. Et, On $(\Delta_{\lambda}^{m},I)-$ statistical convergence of order $\alpha$, Period. Math. Hungar. 71(2) (2015), 135–145.
  • [14] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [15] M. I¸sık, K. E. Akba¸s, On Lamda-statistical convergence of order $\alpha$ in probability, J. Inequal. Spec. Funct. 8(4) (2017), 57–64.
  • [16] M. I¸sık, K. E. Et, On lacunary statistical convergence of order $\alpha$ in probability, AIP Conference Proceedings 1676, 020045 (2015); doi: http://dx.doi.org/10.1063/1.4930471.
  • [17] M. I¸sık, K. E. Akbaş, On Asymptotically Lacunary Statistical Equivalent Sequences of Order $\alpha$ in Probability, ITM Web of Conferences 13, 01024 (2017). DOI: 10.1051/itmconf/20171301024.
  • [18] S. A. Mohiuddine, A. Alotaibi, M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abstr. Appl. Anal., 2002 (2012), Article ID 719729, 9 pp.
  • [19] M. Mursaleen, A. Khan, H. M. Srivastava, K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput., 219 (2013), 6911–6918.
  • [20] F. Nuray, Lamda-strongly summable and $\lambda-$-statistically convergent functions, Iran. J. Sci. Technol. Trans. A Sci., 34 (2010), 335–338.
  • [21] F. Nuray, B. Aydin, Strongly summable and statistically convergent functions, Inform. Technol. Valdymas 1(30) (2004), 74–76.
  • [22] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
  • [23] H. Şengül, M. Et, On I-lacunary statistical convergence of order $\alpha$ of sequences of sets, Filomat 31(8) (2017), 2403–2412.
  • [24] H. Şengül, On Wijsman I-lacunary statistical equivalence of order $(\eta,\mu)$, J. Inequal. Spec. Funct. 9(2) (2018), 92–101.
  • [25] H. Şengül, On $S_{\alpha}^{\beta}\left( \theta\right) -$ convergence and strong $N_{\alpha}^{\beta}\left( \theta,p\right) -$ summability, J. Nonlinear Sci. Appl. 10(9) (2017), 5108–5115.
  • [26] H. Şengül, M. Et, Lacunary statistical convergence of order $(\alpha,\beta)$ in topological groups, Creat. Math. Inform. 2683 (2017), 339–344.
  • [27] H. M. Srivastava, M. Mursaleen, A. Khan, Generalized equi-statistical convergence of positive linear operators and associated approximation theorems, Math. Comput. Modelling 55 (2012), 2040–2051.
  • [28] H. M. Srivastava, M. Et, Lacunary statistical convergence and strongly lacunary summable functions of order $\alpha$; Filomat 31(6) (2017), 1573–1582.
  • [29] R. P. Agnew, On deferred Cesàro mean, Ann. Math.,33 (1932), 413-421.
  • [30] M. Küçükaslan, M. Yılmaztürk On deferred statistical convergence of sequences, Kyungpook Math. J. 56 (2016), 357-366.

Deferred Statistical Convergence in Metric Spaces

Year 2019, Volume: 2 Issue: 3, 189 - 193, 30.12.2019

Mikail Et , Muhammed Cinar , Hacer Şengül

Abstract

In this paper, the concept of deferred statistical convergence is generalized to general metric spaces, and some inclusion relations between deferred strong Ces\`{a}ro summability and deferred statistical convergence are given in general metric spaces.

Keywords

Metric Space Statistical Convergence Deferred statistical convergence

References

  • [1] A. Zygmund, Trigonometric series, Cambridge University Press, Cambridge, London and New York, 1979.
  • [2] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73–74.
  • [3] H. Fast, Sur la convergence statistique, Colloq. Math.,2 (1951), 241–244.
  • [4] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [5] S. Gupta, V. K. Bhardwaj, On deferred f-statistical convergence, Kyungpook Math. J. 58(1) (2018), 91–103.
  • [6] N. L. Braha, H. M. Srivastava, S. A. Mohiuddine, A Korovkin’s type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean, Appl. Math. Comput., 228 (2014), 162–169.
  • [7] M. Çınar, M. Karaka¸s, M. Et, On pointwise and uniform statistical convergence of order $\alpha$ for sequences of functions, Fixed Point Theory Appl. 33(2013), 11.
  • [8] J. S. Connor, The Statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988), 47–63.
  • [9] M. Et, A. Alotaibi, S. A. Mohiuddine, On $(\Delta^{m},I)-$-statistical convergence of order $\alpha$; The Scientific World Journal, 2014, 535419 DOI: 10.1155/2014/535419.
  • [10] M. Et, S. A. Mohiuddine, A. Alotaibi, On $\lambda $-statistical convergence and strongly $\lambda -$summable functions of order $\alpha$, J. Inequal. Appl. 469 (2013), 8.
  • [11] M. Et, B. C. Tripathy, A. J. Dutta, On pointwise statistical convergence of order $\alpha$ of sequences of fuzzy mappings, Kuwait J. Sci. 41(3) (2014), 17–30.
  • [12] M. Et, R. Colak, Y. Altın, Strongly almost summable sequences of order $\alpha$; Kuwait J. Sci. 41(2), (2014), 35–47.
  • [13] E. Savaş, M. Et, On $(\Delta_{\lambda}^{m},I)-$ statistical convergence of order $\alpha$, Period. Math. Hungar. 71(2) (2015), 135–145.
  • [14] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [15] M. I¸sık, K. E. Akba¸s, On Lamda-statistical convergence of order $\alpha$ in probability, J. Inequal. Spec. Funct. 8(4) (2017), 57–64.
  • [16] M. I¸sık, K. E. Et, On lacunary statistical convergence of order $\alpha$ in probability, AIP Conference Proceedings 1676, 020045 (2015); doi: http://dx.doi.org/10.1063/1.4930471.
  • [17] M. I¸sık, K. E. Akbaş, On Asymptotically Lacunary Statistical Equivalent Sequences of Order $\alpha$ in Probability, ITM Web of Conferences 13, 01024 (2017). DOI: 10.1051/itmconf/20171301024.
  • [18] S. A. Mohiuddine, A. Alotaibi, M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abstr. Appl. Anal., 2002 (2012), Article ID 719729, 9 pp.
  • [19] M. Mursaleen, A. Khan, H. M. Srivastava, K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput., 219 (2013), 6911–6918.
  • [20] F. Nuray, Lamda-strongly summable and $\lambda-$-statistically convergent functions, Iran. J. Sci. Technol. Trans. A Sci., 34 (2010), 335–338.
  • [21] F. Nuray, B. Aydin, Strongly summable and statistically convergent functions, Inform. Technol. Valdymas 1(30) (2004), 74–76.
  • [22] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150.
  • [23] H. Şengül, M. Et, On I-lacunary statistical convergence of order $\alpha$ of sequences of sets, Filomat 31(8) (2017), 2403–2412.
  • [24] H. Şengül, On Wijsman I-lacunary statistical equivalence of order $(\eta,\mu)$, J. Inequal. Spec. Funct. 9(2) (2018), 92–101.
  • [25] H. Şengül, On $S_{\alpha}^{\beta}\left( \theta\right) -$ convergence and strong $N_{\alpha}^{\beta}\left( \theta,p\right) -$ summability, J. Nonlinear Sci. Appl. 10(9) (2017), 5108–5115.
  • [26] H. Şengül, M. Et, Lacunary statistical convergence of order $(\alpha,\beta)$ in topological groups, Creat. Math. Inform. 2683 (2017), 339–344.
  • [27] H. M. Srivastava, M. Mursaleen, A. Khan, Generalized equi-statistical convergence of positive linear operators and associated approximation theorems, Math. Comput. Modelling 55 (2012), 2040–2051.
  • [28] H. M. Srivastava, M. Et, Lacunary statistical convergence and strongly lacunary summable functions of order $\alpha$; Filomat 31(6) (2017), 1573–1582.
  • [29] R. P. Agnew, On deferred Cesàro mean, Ann. Math.,33 (1932), 413-421.
  • [30] M. Küçükaslan, M. Yılmaztürk On deferred statistical convergence of sequences, Kyungpook Math. J. 56 (2016), 357-366.
There are 30 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mikail Et 0000-0001-8292-7819

Muhammed Cinar 0000-0002-0958-0705

Hacer Şengül 0000-0003-4453-0786

Publication Date December 30, 2019
Acceptance Date December 12, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Et, M., Cinar, M., & Şengül, H. (2019). Deferred Statistical Convergence in Metric Spaces. Conference Proceedings of Science and Technology, 2(3), 189-193.
AMA Et M, Cinar M, Şengül H. Deferred Statistical Convergence in Metric Spaces. Conference Proceedings of Science and Technology. December 2019;2(3):189-193.
Chicago Et, Mikail, Muhammed Cinar, and Hacer Şengül. “Deferred Statistical Convergence in Metric Spaces”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 189-93.
EndNote Et M, Cinar M, Şengül H (December 1, 2019) Deferred Statistical Convergence in Metric Spaces. Conference Proceedings of Science and Technology 2 3 189–193.
IEEE M. Et, M. Cinar, and H. Şengül, “Deferred Statistical Convergence in Metric Spaces”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 189–193, 2019.
ISNAD Et, Mikail et al. “Deferred Statistical Convergence in Metric Spaces”. Conference Proceedings of Science and Technology 2/3 (December 2019), 189-193.
JAMA Et M, Cinar M, Şengül H. Deferred Statistical Convergence in Metric Spaces. Conference Proceedings of Science and Technology. 2019;2:189–193.
MLA Et, Mikail et al. “Deferred Statistical Convergence in Metric Spaces”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 189-93.
Vancouver Et M, Cinar M, Şengül H. Deferred Statistical Convergence in Metric Spaces. Conference Proceedings of Science and Technology. 2019;2(3):189-93.
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