Research Article
Year 2022,
, 294 - 298, 29.06.2022
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.
References
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- [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,
, 294 - 298, 29.06.2022
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 | Natural Sciences |
| Authors | |
| Publication Date | June 29, 2022 |
| Submission Date | February 8, 2022 |
| Acceptance Date | April 19, 2022 |
| Published in Issue | Year 2022 |