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Properties of J_p-Statistical Convergence

Year 2022, Volume: 43 Issue: 2, 294 - 298, 29.06.2022

Canan Sümbül , Cemal Belen , Mustafa Yıldırım

https://doi.org/10.17776/csj.1064559
Cited By: 5

Abstract

In this study, different characterizations of J_p-statistically convergent sequences are given. The main features of J_p-statistically convergent sequences are investigated and the relationship between J_p-statistically convergent sequences and J_p-statistically Cauchy sequences is examined. The properties provided by the set of bounded and J_p statistical convergent sequences is shown. It is given that the statistical limit is unique. Furthermore, a sequence that J_p-statistical converges to the number L has a subsequence that converges to the same number of L, is shown. The analogs of J_p statistical convergent sequences is studied.

Keywords

Power series method J_p-statistical convergence J_p-statistical Cauchy

References

  • [1] Zygmund A., Trigonometric Series. 3rd.ed. London: Cambridge Univ. Press, (2003),
  • [2] Fast H., Sur la convergence statistique, Colloq. Math., 2 (1951) 241-244.
  • [3] Steinhaus H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951) 73-74.
  • [4] Buck R. C., Generalized asymptotic density, Amer. J. Math., 75 (2) (1953) 335-346.
  • [5] Fridy, J. A., On statistical convergence, Analysis 5 (1985) 301-313.
  • [6] Schoenberg I. J. , The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5) (1959) 361-375.
  • [7] Connor J., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988) 47-63.
  • [8] Connor J., On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32 (1989) 194-198.
  • [9] Belen C., Mursaleen M.,Yildirim M., Statistical A-summability of double sequences and a Korovkin type approximation theorem, Bull. Korean Math. Soc., 49 (4) (2012) 851–861.
  • [10] Belen C., Some Tauberian theorems for weighted means of bounded double sequences, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 63 (1) (2017) 115–122.
  • [11] Burgin M., Duman O., Statistical convergence and convergence in statistics, http://arxiv.org/abs/math/0612179. Retrieved, 2006.
  • [12] Connor J., Kline J., On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl., 197 (2) (1996) 392-399.
  • [13] Çakallı H. and Khan M. K., Summability in topological spaces, Appl. Math. Lett. 24(3) (2011) 348-352.
  • [14] Et M. and Şengul H., Some Cesàro-type summability spaces of order and lacunary statistical convergence of order , Filomat, 28(8) (2014), 1593-1602.
  • [15] Freedman, A. R., Sember, J. J., Densities and summability, Pacific J. Math., 95(2) (1981) 293-305. ]
  • [16] Miller H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(5) (1995) 1811-1819.
  • [17] Šalát, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980) 139-150.
  • [18] Savas E., Mohiuddine S. A., λ-statistically convergent double sequences in probabilistic normed spaces, Math. Slovaca, 62(1) (2012), 99-108.
  • [19] Et M., Baliarsingh P., Şengül Kandemir H., Küçükaslan M., On μ -deferred statistical convergence and strongly deferred summable functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 115(1-34) (2021).
  • [20] Sengül H., Et M., Lacunary statistical convergence of order (α,β) in topological groups, Creat. Math. Inform., 26(3), (2017), 339-344.
  • [21] Sengul H., Et M., f-lacunary statistical convergence and strong f-lacunary summability of order α, Filomat, 32(13) (2018) 4513-4521.
  • [22] Sengul H., Et M., On (λ,I)-statistical convergence of order α of sequences of function, Proc. Nat. Acad. Sci. India Sect. A, 88(2) (2018) 181--186.
  • [23] Ünver M., Abel summability in topological spaces, Monatsh. Math., 178(4) (2015) 633-643.
  • [24] Ünver M., Orhan C., Statistical convergence with respect to power series methods and applications to approximation theory, Numer. Func. Anal Opt., 40(5) (2019) 535-547.
  • [25] Belen C., Yıldırım M., Sümbül C., On Statistical and Strong Convergence with Respect to a Modulus Function and a Power Series Method, Filomat, 34 (12) (2020) 3981-3993.A.
  • [26] Boos J., Classical and modern methods in summability, Oxford University Press, Oxford (2000).

Year 2022, Volume: 43 Issue: 2, 294 - 298, 29.06.2022

Canan Sümbül , Cemal Belen , Mustafa Yıldırım

https://doi.org/10.17776/csj.1064559
Cited By: 5

Abstract

References

  • [1] Zygmund A., Trigonometric Series. 3rd.ed. London: Cambridge Univ. Press, (2003),
  • [2] Fast H., Sur la convergence statistique, Colloq. Math., 2 (1951) 241-244.
  • [3] Steinhaus H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951) 73-74.
  • [4] Buck R. C., Generalized asymptotic density, Amer. J. Math., 75 (2) (1953) 335-346.
  • [5] Fridy, J. A., On statistical convergence, Analysis 5 (1985) 301-313.
  • [6] Schoenberg I. J. , The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5) (1959) 361-375.
  • [7] Connor J., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988) 47-63.
  • [8] Connor J., On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32 (1989) 194-198.
  • [9] Belen C., Mursaleen M.,Yildirim M., Statistical A-summability of double sequences and a Korovkin type approximation theorem, Bull. Korean Math. Soc., 49 (4) (2012) 851–861.
  • [10] Belen C., Some Tauberian theorems for weighted means of bounded double sequences, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 63 (1) (2017) 115–122.
  • [11] Burgin M., Duman O., Statistical convergence and convergence in statistics, http://arxiv.org/abs/math/0612179. Retrieved, 2006.
  • [12] Connor J., Kline J., On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl., 197 (2) (1996) 392-399.
  • [13] Çakallı H. and Khan M. K., Summability in topological spaces, Appl. Math. Lett. 24(3) (2011) 348-352.
  • [14] Et M. and Şengul H., Some Cesàro-type summability spaces of order and lacunary statistical convergence of order , Filomat, 28(8) (2014), 1593-1602.
  • [15] Freedman, A. R., Sember, J. J., Densities and summability, Pacific J. Math., 95(2) (1981) 293-305. ]
  • [16] Miller H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(5) (1995) 1811-1819.
  • [17] Šalát, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980) 139-150.
  • [18] Savas E., Mohiuddine S. A., λ-statistically convergent double sequences in probabilistic normed spaces, Math. Slovaca, 62(1) (2012), 99-108.
  • [19] Et M., Baliarsingh P., Şengül Kandemir H., Küçükaslan M., On μ -deferred statistical convergence and strongly deferred summable functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 115(1-34) (2021).
  • [20] Sengül H., Et M., Lacunary statistical convergence of order (α,β) in topological groups, Creat. Math. Inform., 26(3), (2017), 339-344.
  • [21] Sengul H., Et M., f-lacunary statistical convergence and strong f-lacunary summability of order α, Filomat, 32(13) (2018) 4513-4521.
  • [22] Sengul H., Et M., On (λ,I)-statistical convergence of order α of sequences of function, Proc. Nat. Acad. Sci. India Sect. A, 88(2) (2018) 181--186.
  • [23] Ünver M., Abel summability in topological spaces, Monatsh. Math., 178(4) (2015) 633-643.
  • [24] Ünver M., Orhan C., Statistical convergence with respect to power series methods and applications to approximation theory, Numer. Func. Anal Opt., 40(5) (2019) 535-547.
  • [25] Belen C., Yıldırım M., Sümbül C., On Statistical and Strong Convergence with Respect to a Modulus Function and a Power Series Method, Filomat, 34 (12) (2020) 3981-3993.A.
  • [26] Boos J., Classical and modern methods in summability, Oxford University Press, Oxford (2000).
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Canan Sümbül 0000-0002-8905-1247

Cemal Belen 0000-0002-8832-1524

Mustafa Yıldırım 0000-0002-8880-5457

Submission Date February 8, 2022
Acceptance Date April 19, 2022
Publication Date June 29, 2022
Published in Issue Year 2022 Volume: 43 Issue: 2

Cite

APA Sümbül, C., Belen, C., & Yıldırım, M. (2022). Properties of J_p-Statistical Convergence. Cumhuriyet Science Journal, 43(2), 294-298. https://doi.org/10.17776/csj.1064559

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Statistical convergence with respect to power series method on time scales
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Riesz lacunary uniform integrability and statistical convergence via power series method
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https://doi.org/10.1186/s13660-025-03316-4

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