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

Sevcan Demirkale; Emre Taş

doi:10.36753/mathenot.1212331

Research Article

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

Year 2023, , 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, , 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

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.