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Year 2023, Volume: 11 Issue: 4, 192 - 197, 25.10.2023
https://doi.org/10.36753/mathenot.1200018

Abstract

References

  • [1] Phu, H. X.:Rough convergence in normed linear spaces. Numerical Functional Analysis and Optimization. 22, 201-224 (2001).
  • [2] Phu, H. X.:Rough convergence in infinite dimensional normed spaces. Numerical Functional Analysis and Optimization. 24, 285-301 (2003).
  • [3] Aytar, S.: Rough statistical convergence. Numerical Functional Analysis and Optimization. 29 (3-4), 291-303 (2008).
  • [4] Dündar, E., Çakan, C.: Rough I-convergence. Demonstratio Mathematica. 47 (3), 638-651 (2014).
  • [5] Pal, S. K., Chandra, D., Dutta, S.: Rough ideal convergence. Hacettepe Journal of Mathematics and Statistics. 42(6), 633-640 (2013).
  • [6] Malik, P., Maity, M.: On rough statistical convergence of double sequences in normed linear spaces. Afrika Matematika. 27, 141-148 (2016).
  • [7] Ki¸si, Ö., Dündar, E.: Rough I2-lacunary statistical convergence of double sequences. Journal of Inequalities and Applications. 2018, 230 (2018).
  • [8] Debnath, S., Rakshit, D.: Rough convergence in metric spaces. In: New Trends in Analysis and Interdisciplinary Applications. 449-454 (2017).
  • [9] Arslan, M., Dündar, E.: On rough convergence in 2-normed spaces and some properties. Filomat. 33 (16), 5077-5086 (2019).
  • [10] Dündar, E., Ulusu, U.: On rough convergence in amenable semigroups and some properties. Journal of Intelligent & Fuzzy Systems. 41, 2319-2324 (2021).
  • [11] Ki¸si, Ö., Dündar, E.: Rough I-statistical convergence. Journal of Applied Mathematics & Informatics. 40 (3-4), 619-632 (2022).
  • [12] Ölmez, Ö., Akçay, F. G., Aytar, S.: On the rough convergence of a sequence of sets. Electronic Journal of Mathematical Analysis and Applications. 10 (1), 167-174 (2022).
  • [13] Subramanian, N., Esi, A.: Wijsman rough convergence of triple sequences. Matematychni Studii. 48, 171-179 (2017).
  • [14] Powell, R. E., Shah, S. M.:Summability theory and applications. Van Nostrand Reinhold. London (1972).

A Note on Rough Abel Convergence

Year 2023, Volume: 11 Issue: 4, 192 - 197, 25.10.2023
https://doi.org/10.36753/mathenot.1200018

Abstract

In this paper, we define a new type of Abel convergence by using the rough convergence of a sequence. We also obtained some results for this convergence.

References

  • [1] Phu, H. X.:Rough convergence in normed linear spaces. Numerical Functional Analysis and Optimization. 22, 201-224 (2001).
  • [2] Phu, H. X.:Rough convergence in infinite dimensional normed spaces. Numerical Functional Analysis and Optimization. 24, 285-301 (2003).
  • [3] Aytar, S.: Rough statistical convergence. Numerical Functional Analysis and Optimization. 29 (3-4), 291-303 (2008).
  • [4] Dündar, E., Çakan, C.: Rough I-convergence. Demonstratio Mathematica. 47 (3), 638-651 (2014).
  • [5] Pal, S. K., Chandra, D., Dutta, S.: Rough ideal convergence. Hacettepe Journal of Mathematics and Statistics. 42(6), 633-640 (2013).
  • [6] Malik, P., Maity, M.: On rough statistical convergence of double sequences in normed linear spaces. Afrika Matematika. 27, 141-148 (2016).
  • [7] Ki¸si, Ö., Dündar, E.: Rough I2-lacunary statistical convergence of double sequences. Journal of Inequalities and Applications. 2018, 230 (2018).
  • [8] Debnath, S., Rakshit, D.: Rough convergence in metric spaces. In: New Trends in Analysis and Interdisciplinary Applications. 449-454 (2017).
  • [9] Arslan, M., Dündar, E.: On rough convergence in 2-normed spaces and some properties. Filomat. 33 (16), 5077-5086 (2019).
  • [10] Dündar, E., Ulusu, U.: On rough convergence in amenable semigroups and some properties. Journal of Intelligent & Fuzzy Systems. 41, 2319-2324 (2021).
  • [11] Ki¸si, Ö., Dündar, E.: Rough I-statistical convergence. Journal of Applied Mathematics & Informatics. 40 (3-4), 619-632 (2022).
  • [12] Ölmez, Ö., Akçay, F. G., Aytar, S.: On the rough convergence of a sequence of sets. Electronic Journal of Mathematical Analysis and Applications. 10 (1), 167-174 (2022).
  • [13] Subramanian, N., Esi, A.: Wijsman rough convergence of triple sequences. Matematychni Studii. 48, 171-179 (2017).
  • [14] Powell, R. E., Shah, S. M.:Summability theory and applications. Van Nostrand Reinhold. London (1972).
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Öznur Ölmez 0000-0001-6563-8732

Ulas Yamanci 0000-0002-4709-0993

Early Pub Date August 8, 2023
Publication Date October 25, 2023
Submission Date November 6, 2022
Acceptance Date December 5, 2022
Published in Issue Year 2023 Volume: 11 Issue: 4

Cite

APA Ölmez, Ö., & Yamanci, U. (2023). A Note on Rough Abel Convergence. Mathematical Sciences and Applications E-Notes, 11(4), 192-197. https://doi.org/10.36753/mathenot.1200018
AMA Ölmez Ö, Yamanci U. A Note on Rough Abel Convergence. Math. Sci. Appl. E-Notes. October 2023;11(4):192-197. doi:10.36753/mathenot.1200018
Chicago Ölmez, Öznur, and Ulas Yamanci. “A Note on Rough Abel Convergence”. Mathematical Sciences and Applications E-Notes 11, no. 4 (October 2023): 192-97. https://doi.org/10.36753/mathenot.1200018.
EndNote Ölmez Ö, Yamanci U (October 1, 2023) A Note on Rough Abel Convergence. Mathematical Sciences and Applications E-Notes 11 4 192–197.
IEEE Ö. Ölmez and U. Yamanci, “A Note on Rough Abel Convergence”, Math. Sci. Appl. E-Notes, vol. 11, no. 4, pp. 192–197, 2023, doi: 10.36753/mathenot.1200018.
ISNAD Ölmez, Öznur - Yamanci, Ulas. “A Note on Rough Abel Convergence”. Mathematical Sciences and Applications E-Notes 11/4 (October 2023), 192-197. https://doi.org/10.36753/mathenot.1200018.
JAMA Ölmez Ö, Yamanci U. A Note on Rough Abel Convergence. Math. Sci. Appl. E-Notes. 2023;11:192–197.
MLA Ölmez, Öznur and Ulas Yamanci. “A Note on Rough Abel Convergence”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 4, 2023, pp. 192-7, doi:10.36753/mathenot.1200018.
Vancouver Ölmez Ö, Yamanci U. A Note on Rough Abel Convergence. Math. Sci. Appl. E-Notes. 2023;11(4):192-7.

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