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.
[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
[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).