ON ROUGH $I^*$ AND $I^K$-CONVERGENCE OF SEQUENCES IN NORMED LINEAR SPACES

Amar Kumar Banerjee, Anirban Paul

DOI Number
https://doi.org/10.22190/FUMI210921038B
First page
541
Last page
557

Abstract


In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough $I$-convergence with both of rough $I^*$-convergence and rough $I^K$-convergence.

Keywords

rough $I^*$-convergence, rough $I^K$-convergence, linear space

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References


F. G. Arenas: Alexandroff spaces. Acta Math. Univ. Comenian. 68(1) (1999), 17–25.

A. K. Banerjee and A. Banerjee: I-convergence classes of sequences and nets in topological spaces. Jordan Journal of Mathematics and Statistics (JJMS). 11(1) (2018), 13–31.

A. K. Banerjee and R. Mondal. A note on convergence of double sequences in a topological space. Mat. Vesnik. 69(2) (2017), 144–152.

A. K. Banerjee and R. Mondal: Rough convergence of sequences in a cone metric space. The Journal of Analysis. 27 (2019), 1179—1188.

A. K. Banerjee and A. Banerjee: A study on I-Cauchy sequences and I-divergence in S-metric spaces. Malaya Journal of Matematik(MJM). 6(2) (2018), 326–330.

L. Bukovsky and P. Das and J. Supina: Ideal quasi-normal convergence and related notions. Colloq. Math. 146(2) (2017), 265–281.

C. Buck: Generalised asymptotic density. Amer. J. Math. 75 (1953), 335–346.

H. Cakalli: A new approach to statistically quasi Cauchy sequences. Maltepe Journal of Mathematics. 1(1) (2019), 1–8.

P. Das and S. Sengupta and J. Supina: IK-convergence of sequences of functions. Mathematica Slovaca. 69(5) (2019), 1137–1148.

P. Das and M. Sleziak and V. Toma: IK-Cauchy functions. Topology and its Applications. 173 (2014), 9–27.

E. Dundar and C. Cakan: Rough I-convergence. Demonstratio Mathematica. 47(3) (2014), 638–651.

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

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

P. Kostyrko and M. Macaj and T. Salat: Statistical convergence and Iconvergence. 1999, Unpublished, http://thales.doa.fmph.uniba.sk/macaj/ICON.pdf.

P. Kostyrko and T. Salat and W. Wilczynski: I-convergence. Real Analysis Exchange. 26(2) (2000/2001), 669–686.

C. Kuratowski: Topologie I. PWN Warszawa, 1958.

P. Kostyrko and M. Macaj and T. Salat and M. Sleziak: I-convergence and extremal I-limit points. Math Slovaca. 55 (2005), 443–464.

J. L. Kelley: General Topology. Springer-Verlag, New York, 1955.

B. K. Lahiri and P. Das: Further results on I-limit superior and I-limit inferior. Math. Commun. 8 (2003), 151–156.

B. K. Lahiri and P. Das: I and I∗-convergence in topological spaces. Math. Bohemica. 130(2) (2005), 153–160.

M. Macaj and M. Sleziak: IK-convergence. Real Analysis Exchange. 36(1) (2010/2011), 177–194.

A. Nabiev and S. Pehlivan and M. Gurdal: On I-Cauchy sequences. Taiwanese J. Math. 12(2) (2007), 569–576.

H. X. Phu: Rough convergence in normed linear space. Numer. Funct. Anal. Optim. 22 (2001), 199–222.

S. K. Pal and D. Chandra and S. Dutta: Rough ideal convergence. Hacettepe Journal of Mathematics and Statistics. 42(6) (2013), 633–640.

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

H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2 (1951), 73–74.

I. J. Schoenberg: The integrability of certain functions and related summability methods. Amer. Math. Monthly. 66(5) (1959), 361–375.

H. S.engul Kandemır: On I-deferred statical convergence in topological groups. Maltepe Journal of Mathematics. I(2) (2019), 48–55.

I. Taylan: Abel statistical delta quasi Cauchy sequences of real numbers. Maltepe Journal of Mathematics. 1(1) (2019), 18–23.

N. Tok and M. Basarir: On the lambda alpha h Statistical Convergence of the Functions Defined on the Time Scale. Proceedings of International Mathematical Sciences. I(1) (2019), 1–10.

A. Zygmund: Trigonometric Series. Cambridge Univ. Press, Cambridge, UK, 1979.




DOI: https://doi.org/10.22190/FUMI210921038B

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