I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces

Year 2019, Volume: 68 Issue: 2, 2324 - 2332, 01.08.2019

Ekrem Savaş , Ulas Yamanci , Mehmet Gürdal

https://doi.org/10.31801/cfsuasmas.573396

Cited By: 1

Abstract

In this paper, we introduce new concepts of I-statistical convergence and I-lacunary statistical convergence using weighted density via modulus functions. Also, we study the relationship between them and obtain some interesting results.

Keywords

I-statistical convergence, I-lacunary statistical convergence, 2-normed spaces, weight function

References

• Balcerzak, M., Das, P., Filipczak, M. and Swaczyna, J., Generalized kinds of density and the associated ideals, Acta Math. Hungar. 147, (2015), 97--115.
• Bose, K., Das, P. and Kwela, A., Generating new ideals using weighted density via modulus functions, Indag. Math. 29(5), (2018), 1196--1209.
• Das, P., Savaş E. and Ghosal, S., On generalized of certain summability methods using ideals, Appl. Math. Lett. 26, (2011), 1509--1514.
• Fast, H., Sur la convergence statistique, Colloq. Math., 2(1951), 241--244.
• Fridy, J. A. and Orhan, C., Lacunary statistical convergence, Pacific J. Math. 160, (1993), 43--51.
• Gähler, S., 2-metrische Räume und ihre topologische struktur, Math. Nachr. 26, (1993), 115--148.
• Gürdal, M., On ideal convergent sequences in 2-normed spaces, Thai J. Math. 4(1), (2006), 85--91.
• Gürdal, M. and Açık, I., On I-Cauchy sequences in 2-normed spaces, Math. Inequal. Appl. 2(1), (2008), 349--354.
• Gürdal, M. and Yamancı, U., Statistical convergence and some questions of operator theory, Dynam. Syst. Appl. 24, (2015), 305--312.
• Kostyrko, P.,Šalát, T. and Wilezynski, W., I-Convergence, Real Anal. Exchange 26(2), (2000), 669--686.
• Mursaleen, M. and Alotaibi, A., On I-convergence in random 2-normed space, Math. Slovaca 61(6), (2011), 933--940.
• Nabiev, A., Pehlivan, S. and Gürdal, M., On I-Cauchy sequences, Taiwanese J. Math. 11(2), (2007), 569--576.
• Şahiner, A., Gürdal, M., Saltan, S. and Gunawan, H., Ideal Convergence in 2-normed Spaces, Taiwanese J. Math. 11(4), (2007), 1477--1484.
• Savaş, E., On lacunary strong σ-convergence, Indian J. Pure Appl. Math. 21, (1990), 359--365.
• Savaş, E. and Karakaya, V., Some new sequence spaces defined by lacunary sequences, Math. Slovaca 57, (2007), 393--399.
• Savaş, E. and Patterson, R. F., Double σ-convergence lacunary statistical sequences, J. Comput. Anal. Appl. 11, (2009), 610--615.
• Savaş, E. and Das, P., A generalized statistical convergence via ideals, Appl. Math. Letters 24, (2011), 826--830.
• Savaş, E., Das, P. and Dutta, S., A note on strong matrix summability via ideals, Appl. Math Letters 25, (2012) 733--738.
• Savaş, E., On I-lacunary statistical convergence of order α for sequences of sets, Filomat 29, (2015), 1223--1229.
• Schoenberg, I. J., The integrability of certain functions and related summability methods, Am. Math. Mon. 66, (1959), 361--375.
• Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, (1951), 73--74.
• Ulusu, U. and Nuray, F., Lacunary statistical convergence of sequence of sets, Progress Appl. Math. 4, (2012), 99--109.
• Ulusu, U. and Dündar, E., I-lacunary statistical convergence of sequences of sets, Filomat 28(8), (2014), 1567--1574.
• Yamancı, U. and Gürdal, M., I-statistical convergence in 2-normed space, Arab J. Math. Sci. 20(1), (2014), 41--47.
• Yamancı, U. and Gürdal, M., Statistical convergence and operators on Fock space, New York J. Math. 22, (2016), 199--207.
• Yegül, S. and Dündar, E., On statistical convergence of sequences of functions in 2-normed spaces, J. Classical Anal. 10(1), (2017), 49--57.