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ON I AND I*-CAUCHY CONDITIONS IN C*-ALGEBRA VALUED METRIC SPACES

  • Received : 2020.07.11
  • Accepted : 2021.08.06
  • Published : 2021.09.30

Abstract

The idea of C*-algebra valued metric spaces was given by Ma, Jiang and Sun. In this paper we have studied the ideas of I-Cauchy and I*-Cauchy sequences and their properties in such spaces and also we give the idea of C*-algebra valued normed spaces.

Keywords

References

  1. M. Balacerzak, K. Dems, and A. Komisarki, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. App. 328 (1) (2007), 715-729. https://doi.org/10.1016/j.jmaa.2006.05.040
  2. A. K. Banerjee, and A. Banerjee, A note on I-convergence and I*-convergence of sequences and nets in topological spaces, Mat. Vesnik. 67 (3) (2015), 212-221.
  3. A. K. Banerjee, and A. Dey, Metric spaces and complex Analysis, New Age International(P) Ltd Publishers, 2008.
  4. A. K. Banerjee, and R. Mondal, A note on convergence of double sequences in a topological space, Mat. Vesnik. 69 (2) (2017), 144-152.
  5. P. Das, and S. K. Ghosal, Some further result on I-Cauchy sequences and condition (AP), Comp. Math. Appl. 59 (2010), 2597-2600. https://doi.org/10.1016/j.camwa.2010.01.027
  6. P. Das, P. Kostyrko, W. Wilczynski, and P. Malik, I and I*-convergence of double sequences, Math. Slovaca. 58 (5) (2008), 605-620. https://doi.org/10.2478/s12175-008-0096-x
  7. K. Dems, On I-Cauchy sequences, Real Anal. Exch. 30(1)(2004/2005), 123-128. https://doi.org/10.14321/realanalexch.30.1.0123
  8. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  9. J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313. https://doi.org/10.1524/anly.1985.5.4.301
  10. P. Kostyrko, T. Salat, and W. Wilczynski, I-convergence, Real Analysis Exchange. 26 (2) (2000/2001), 669-686. https://doi.org/10.2307/44154069
  11. C. Kuratowski, Topologie. I., PWN Warszawa, 1958.
  12. B. K. Lahiri, and P. Das, Further results on I-limit superior and I-limit inferior, Math. Commun. 8 (2003), 151-156.
  13. B. K. Lahiri, and P. Das, I and I*-convergence in topological spaces, Math. Bohemica. 130 (2) (2005), 153-160. https://doi.org/10.21136/MB.2005.134133
  14. G. J. Murphy, C*-Algebras and Operator Theory, Academic Press, London, 1990.
  15. Z. Ma, L. Jiang, and H. Sun, C*-algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. 206 (2014), 2014.
  16. A. Nabiev, S. Pehlivan, and M. Gurdal, On I-Cauchy sequences, Taiwanese J. Math. 12 (2) (2007), 569-576.
  17. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca. 30 (1980), 139-150.
  18. H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73-74. https://doi.org/10.4064/cm-2-2-98-108
  19. D. Turkoglo, M. Abuloha, and T. Abdeljawad, Some theorems in cone metric spaces, Journal of concrete and applicable mathematics. 10 (2012).