Properties of J_p-Statistical Convergence

Canan Sümbül; Cemal Belen; Mustafa Yıldırım

doi:10.17776/csj.1064559

EN

Properties of J_p-Statistical Convergence

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

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).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Canan Sümbül
0000-0002-8905-1247
Türkiye

Cemal Belen
0000-0002-8832-1524
Türkiye

Mustafa Yıldırım ^*
0000-0002-8880-5457
Türkiye

Publication Date

June 29, 2022

Submission Date

February 8, 2022

Acceptance Date

April 19, 2022

Published in Issue

Year 2022 Volume: 43 Number: 2

DOI

https://doi.org/10.17776/csj.1064559

IZ

https://izlik.org/JA33FW48LZ

Cite

RIS / Bibtex

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

Properties of J_p-Statistical Convergence

Properties of J_p-Statistical Convergence

Abstract

Keywords

Öz

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

On statistical limit points with respect to power series methods and modulus functions

On power series statistical convergence and new uniform integrability of double sequences

On Continuities via P-Statistical Convergence

Statistical convergence with respect to power series method on time scales

Riesz lacunary uniform integrability and statistical convergence via power series method

On difference <inline-formula><tex-math id="M1">$ J_{a,b}- $</tex-math></inline-formula>statistical convergence