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Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces

Year 2023, Volume: 11 Issue: 2, 104 - 111, 30.06.2023

Sevcan Demirkale , Emre Taş

https://doi.org/10.36753/mathenot.1212331

Abstract

In the present paper, $P-$distributional convergence which is defined by power series method has been introduced. We give equivalent expressions for $P-$distributional convergence of spliced sequences. Moreover, convergence of a bounded $\infty$-spliced sequence via power series method is represented in terms of Bochner integral in Banach spaces.

Keywords

P-distributional convergence P-density Power series P-statistical convergence spliced sequences

References

  • [1] Osikiewicz, J. A.: Summability of spliced sequences. Rocky Mountain Journal of Mathematics. 35, 977-996 (2005).
  • [2] Unver, M.: Abel summability in topological spaces. Monatshefte für Mathematik. 178, 633-643 (2015).
  • [3] Unver, M., Khan, M., Orhan, C.: A-distributional summability in topological spaces. Positivity. 18, 131-145 (2014).
  • [4] Yurdakadim, T., Ünver, M.: Some results concerning the summability of spliced sequences. Turkish Journal of Mathematics. 40, 1134-1143 (2016).
  • [5] Bartoszewicz, A., Das, P., Gła¸b, S.: On matrix summability of spliced sequences and A-density. Linear Algebra and its Applications, 487, 22-42 (2015).
  • [6] Fast, H.: Sur la convergence statistique. Colloquium Mathematicae. 2, 241-244 (1951).
  • [7] Fridy, J. A.: On statistical convergence. Analysis. 5, 301-314 (1985).
  • [8] Šalát, T.: On statistically convergent sequences of real numbers. Mathematica Slovaca. 30, 139-150 (1980).
  • [9] Boos, J.: Classical and modern methods in summability. Oxford University Press. UK (2000).
  • [10] Unver, M., Orhan, C.: Statistical convergence with respect to power series methods and applications to approximation theory. Numerical Functional Analysis and Optimization. 40, 535-547 (2019).
  • [11] Bayram, N. ¸S.: Criteria for statistical convergence with respect to power series methods. Positivity. 25, 1097-1105 (2021).

Year 2023, Volume: 11 Issue: 2, 104 - 111, 30.06.2023

Sevcan Demirkale , Emre Taş

https://doi.org/10.36753/mathenot.1212331

Abstract

References

  • [1] Osikiewicz, J. A.: Summability of spliced sequences. Rocky Mountain Journal of Mathematics. 35, 977-996 (2005).
  • [2] Unver, M.: Abel summability in topological spaces. Monatshefte für Mathematik. 178, 633-643 (2015).
  • [3] Unver, M., Khan, M., Orhan, C.: A-distributional summability in topological spaces. Positivity. 18, 131-145 (2014).
  • [4] Yurdakadim, T., Ünver, M.: Some results concerning the summability of spliced sequences. Turkish Journal of Mathematics. 40, 1134-1143 (2016).
  • [5] Bartoszewicz, A., Das, P., Gła¸b, S.: On matrix summability of spliced sequences and A-density. Linear Algebra and its Applications, 487, 22-42 (2015).
  • [6] Fast, H.: Sur la convergence statistique. Colloquium Mathematicae. 2, 241-244 (1951).
  • [7] Fridy, J. A.: On statistical convergence. Analysis. 5, 301-314 (1985).
  • [8] Šalát, T.: On statistically convergent sequences of real numbers. Mathematica Slovaca. 30, 139-150 (1980).
  • [9] Boos, J.: Classical and modern methods in summability. Oxford University Press. UK (2000).
  • [10] Unver, M., Orhan, C.: Statistical convergence with respect to power series methods and applications to approximation theory. Numerical Functional Analysis and Optimization. 40, 535-547 (2019).
  • [11] Bayram, N. ¸S.: Criteria for statistical convergence with respect to power series methods. Positivity. 25, 1097-1105 (2021).
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sevcan Demirkale 0000-0003-0739-5044

Emre Taş 0000-0002-6569-626X

Publication Date June 30, 2023
Submission Date November 30, 2022
Acceptance Date January 19, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

APA Demirkale, S., & Taş, E. (2023). Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces. Mathematical Sciences and Applications E-Notes, 11(2), 104-111. https://doi.org/10.36753/mathenot.1212331
AMA Demirkale S, Taş E. Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces. Math. Sci. Appl. E-Notes. June 2023;11(2):104-111. doi:10.36753/mathenot.1212331
Chicago Demirkale, Sevcan, and Emre Taş. “Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces”. Mathematical Sciences and Applications E-Notes 11, no. 2 (June 2023): 104-11. https://doi.org/10.36753/mathenot.1212331.
EndNote Demirkale S, Taş E (June 1, 2023) Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces. Mathematical Sciences and Applications E-Notes 11 2 104–111.
IEEE S. Demirkale and E. Taş, “Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces”, Math. Sci. Appl. E-Notes, vol. 11, no. 2, pp. 104–111, 2023, doi: 10.36753/mathenot.1212331.
ISNAD Demirkale, Sevcan - Taş, Emre. “Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces”. Mathematical Sciences and Applications E-Notes 11/2 (June 2023), 104-111. https://doi.org/10.36753/mathenot.1212331.
JAMA Demirkale S, Taş E. Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces. Math. Sci. Appl. E-Notes. 2023;11:104–111.
MLA Demirkale, Sevcan and Emre Taş. “Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 2, 2023, pp. 104-11, doi:10.36753/mathenot.1212331.
Vancouver Demirkale S, Taş E. Statistical Convergence of Spliced Sequences in Terms of Power Series on Topological Spaces. Math. Sci. Appl. E-Notes. 2023;11(2):104-11.
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