Properties of J_p-Statistical Convergence

Temel Bulgular & Veri: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.

💡

Sonuç & Katkı:The analogs of J_p statistical convergent sequences is studied.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Power series method · J_p-statistical convergence · J_p-statistical Cauchy

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.

Anahtar kelimeler

Power series method J_p-statistical convergence J_p-statistical Cauchy

🔖

Bu Makaleye Atıf Yap

SÜMBÜL, C., BELEN, C., YILDIRIM, M. (2022). Properties of J_p-Statistical Convergence. Cumhuriyet Science Journal, Cilt: 43 Sayı: 2, 294–298. https://ajindex.com/articles/960290

📄 Tam Metin PDF Okuyucu

Yeni Sekmede Aç ↗

↗Yeni Sekme

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (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