A Note on Rough Abel Convergence

Year 2023, Volume: 11 Issue: 4, 192 - 197, 25.10.2023

Öznur Ölmez , Ulas Yamanci

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.

Keywords

Abel convergence, Abel summability, rough convergence, rough limits.

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).