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Article

On μ– statistical uniform convergence and Dini’s theorem

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Pages 7744-7751 | Received 14 Dec 2021, Accepted 22 Mar 2022, Published online: 05 Apr 2022

References

  • Balcerzak, M., K. Dems, and A. Komisarski. 2007. Statistical convergence and ideal convergence for sequences of functions. Journal of Mathematical Analysis and Applications 328 (1):715–29. doi:10.1016/j.jmaa.2006.05.040.
  • Bilalov, B. T., and T. Y. Nazarova. 2015. Statistical convergence of functional sequences. Rocky Mountain Journal of Mathematics 45 (5):1413–23.
  • Connor, J. 1990. Two valued measures and summability. Analysis 10 (4):373–86. doi:10.1524/anly.1990.10.4.373.
  • Connor, J., and K. G. Grosse-Erdmann. 2003. Sequential definitions of continuity for real functions. The Rocky Mountain Journal of Mathematics 33 (1):93–121.
  • Duman, O., and C. Orhan. 2004. Statistically convergent function sequences. Czechoslovak Mathematical Journal 54 (2):413–22. doi:10.1023/B:CMAJ.0000042380.31622.39.
  • Fast, H. 1951. Sur la convergence statistique. Colloquium Mathematicum 2 (3–4):241–4. doi:10.4064/cm-2-3-4-241-244.
  • Freedman, A. R., and J. J. Sember. 1981. Densities and summability. Pacific Journal of Mathematics 95 (2):293–305. doi:10.2140/pjm.1981.95.293.
  • Fridy, J. A. 1985. On statistical convergence. Analysis 5 (4):301–13. doi:10.1524/anly.1985.5.4.301.
  • Fridy, J. A., and C. Orhan. 1997. Statistical limit superior and limit inferior. Proceedings of the American Mathematical Society 125 (12):3625–31. doi:10.1090/S0002-9939-97-04000-8.
  • Kostyrko, P., T. Šalát, and W. Wilczyński. 2000/2001. I-convergence. Real Analysis Exchange 26 (2):669–85. doi:10.2307/44154069.
  • Rudin, W. 1976. Principles of mathematical analysis. Vol. 3. New York: Mc Graw Hill Companies, Inc.
  • Šalát, T. 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca 30 (2):139–50.
  • Steinhaus, H. 1951. Sur la convergence ordinaire et la convergence asymtotique. Colloquium Mathematicum 2:73–4.
  • Wilczyński, W. 1999. Statistical convergence of sequences of functions. Real Analysis Exchange 25:49. doi:10.2307/44153029.
  • Wu, Z. 2019. Two convergence theorems and an extension of the ratio test for a series. Mathematics Magazine 92 (3):222–7. doi:10.1080/0025570X.2019.1560841.
  • Wu, Z. 2020. Uniform convergence theorems motivated by Dini’s Theorem for a sequence of functions. Journal of Mathematical Analysis 11 (6):27–36.

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