Double Lacunary Statistical Convergence of Order α in Topological Groups via Ideal

Authors

  • Ekrem Savas Department of Mathematics, Usak University, Usak

DOI:

https://doi.org/10.26713/cma.v9i3.781

Keywords:

Double lacunary, Ideal double lacunary statistical convergence, Topological groups

Abstract

Recently, I-lacunary double statistical convergence in topological groups is presented by Savas [31]. In this paper, we extend the concepts of I-double statistical convergence and I-double lacunary statistical convergence to the concepts of I-double statistical convergence and I-double lacunary statistical convergence of order α, 0<α1. We also investigate some inclusion relations between I-double statistical of order α and I-double lacunary double statistical convergence of order α.

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References

S. Bhunia, P. Das and S. Pal, Restricting statistical convergenge, Acta Math. Hungar 134 (1-2) (2012), 153 – 161.

C. Cakan, B. Altay and H. Coskun, Double lacunary density and lacunary statistical convergence of double sequences, Studia Scientiarum Math. Hung. 47 (1) (2010), 35 – 45.

H. í‡akalli, On Statistical Convergence in topological groups, Pure and Appl. Math. Sci. 43 (1-2) (1996), 27 – 31.

H. í‡akalli, Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math. 26 (2) (1995), 113 – 119.

H. í‡akalli and E. Savas, Statistical convergence of double sequence in topological groups, J. Comp. Anal. Appl. 12 (2) (2010), 421 – 426.

R. Colak, Statistical convergence of order (alpha), in Modern Methods in Analysis and its Applications, New Delhi, India, Anamaya Pub., 121 – 129 (2010).

R. Colak and C.A. Bektas, -statistical convergence of order (alpha), Acta Math. Scientia 31B (3) (2011), 953 – 959.

P. Das, E. Savas and S.K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters 24 (2011), 1509 – 1514.

K. Dems, On I-Cauchy sequences, Real Anal. Exchance 30 (2004-2005), 123 – 128.

H. Fast, Sur la convergence statistique, Colloq Math. 2 (1951), 241 – 244.

J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), 43 – 51.

J.A. Fridy, On statistical convergence, Analysis 5 (1985), 301 – 313.

M. Gurdal and E. Savas, A-cluster points via ideals, Ukrainian Mathematical Journal 69 (3) (2017), 324 – 331.

P. Kostyrko, T. Å alát and W. Wilczynki, I-convergence, Real Anal. Exchange 26 (2) (2000/2001), 669 – 685.

G.D. Maio and L.D.R. Kocinac, Statistical convergence in topology, Topology Appl. 156 (2008), 28 – 45.

Mursaleen and O.H. Edely, Statistical convergence ofdouble sequences, J. Math. Anal. Appl. 288 (1) (2003), 223 – 231.

M. Mursaleen, C. Cakan, S.A. Mohiuddine and E. Savas, Generalized statistical convergence and statistical core of double sequences, Acta Math. Sinica 26 (11) (2010), 2131 – 2144.

A. Nabiev, S. Pehlivan and M. Gurdal, On I-Cauchy sequences, Taiwanese J. Math. 11 (2) (2007), 569 – 566.

R.F. Patterson and E. Savas, Lacunary statistical convergence of double sequences, Math. Commun. 10 (2005), 55 – 61.

A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Annalen 53 (1900), 289 – 321.

T. Å alát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139 – 150.

E. Savas and R.F. Patterson, Double sequence spaces defined by Orlicz functions, Iran. J. Sci. Technol. Trans. A Sci. 31 (2) (2007), 183 – 188.

E. Savas, I-statistically convergent sequences in topological groups, International conference "Kangro-100 – Methods of Analysis and Algebra”, dedicated to the Centennial of Professor Gunnar Kangro, Tartu, Estonia, on September 1-6, 2013.

E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), 826 – 830.

E. Savas, P. Das and S. Dutta, A note on strong matrix summability via ideals, Appl. Math Lett. 25 (4) (2012), 733 – 738.

E. Savas, A sequence spaces in 2-normed space defined by ideal convergence and an Orlicz function, Abstr. Appl. Anal. 2011 (2011), Art. ID 741382, 9 p.

E. Savas, On some new sequence spaces in 2-normed spaces using ideal convergence and an Orlicz function, J. Inequal. Appl. 2010 (2010), Art. ID 482392, 8 p.

E. Savas, I-double Statistical Convergence of Order (alpha) in Topological Groups, Ukrainian Math. Journal 68 (9) (2017), 1437 – 1446.

E. Savas, Lacunary statistical convergence of double sequences in topological groups, J. Inequal. Appl., Article ID 480, published December 2, 2014.

E. Savas, Iµ-statistically convergent sequences in topological groups, Mat. Bilten 39 (2) (2015), 19 – 28.

E. Savas, Double Lacunary Statistical Convergence in Topological Groups Via Ideal, presented for the 30th International Conference of The Jangjeon Mathematical Society (ICJMS'2017), July 12-15, 2017, Algeria.

E. Savas, On some new double lacunary sequences spaces via Orlicz function, J. Comput. Anal. Appl. 11 (3) (2009), 423 – 430.

E. Savas and R.F. Patterson, Some double lacunary sequence spaces defined by Orlicz functions, Southeast Asian Bull. Math. 35 (1) (2011), 103 – 110.

E. Savas and R.F. Patterson, Double (sigma)-convergence lacunary statistical sequences, J. Comput. Anal. Appl. 11 (4) (2009), 610 – 615.

E. Savas and M. Gurdal, I-statistical convergence in probabilistic normed spaces, Scientific Bulletin-Series A Applied Mathematics and Physics 77 (4) (2015), 195 – 204.

E. Savas, I-double statistically convergent sequences in topological groups, Communications in Computer and Information Science 655 (2017), 349 – 357.

E. Savas and R. Savas, Double lacunary statistical convergence of order (alpha), Indian J. Math. 57 (1) (2015), 1 – 15.

I.J. Schoenberg, The integrability methods, Amer. Math. Monthly 66 (1959), 361 – 375.

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Published

25-09-2018
CITATION

How to Cite

Savas, E. (2018). Double Lacunary Statistical Convergence of Order α in Topological Groups via Ideal. Communications in Mathematics and Applications, 9(3), 265–275. https://doi.org/10.26713/cma.v9i3.781

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Section

Research Article