On absolute summability of infinite series and Fourier series

Özarslan, Hikmet Seyhan

doi:10.2478/aupcsm-2023-0010

Abstract

In the present paper, a theorem on θ −|T; δ|_k summability method of an infinite series is proved, and also by using this method, a result on summability of a trigonometric Fourier series is obtained.

References

Bor, Hüseyin. “On two summability methods.” Math. Proc. Cambridge Philos. Soc. 97, no. 1 (1985): 147-149. Cited on 128.
Search in Google Scholar Back to article
Bor, Hüseyin. “On the absolute Riesz summability factors.” Rocky Mountain J. Math. 24, no. 4 (1994): 1263-1271. Cited on 129.
Search in Google Scholar Back to article
Bor, Hüseyin. “Some new results on absolute Riesz summability of infinite series and Fourier series.” Positivity 20, no. 3 (2016): 599-605. Cited on 128 and 133.
Search in Google Scholar Back to article
Bor, Hüseyin. “A new note on factored infinite series and trigonometric Fourier series.” C. R. Math. Acad. Sci. Paris 359 (2021): 323-328. Cited on 128.
Search in Google Scholar Back to article
Bor, Hüseyin. “Factored infinite series and Fourier series involving almost increasing sequences.” Bull. Sci. Math. 169 (2021): Paper No. 102990, 8 pp. Cited on 128.
Search in Google Scholar Back to article
Chen, Kien-Kwong. “Functions of bounded variation and the Cesàro means of a Fourier series.” Acad. Sinica Science Record 1 (1945): 283-289. Cited on 133.
Search in Google Scholar Back to article
Hardy, Godfrey Harold. Divergent Series. Oxford: Oxford University Press, 1949. Cited on 128.
Search in Google Scholar Back to article
Kartal, Ba§dagül. “Generalized absolute Riesz summability of infinite series and Fourier series.” Inter. J. Anal. Appl. 18, no. 6 (2020): 957-964. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “Local properties of factored Fourier series.” Int. J. Comp. Appl. Math. 1, no. 1 (2006): 93-96. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan, and Ba§dagül Kartal. “A generalization of a theorem of Bor.” J. Inequal. Appl. 179 (2017): 8pp. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “A new study on generalised absolute matrix summability methods.” Maejo Int. J. Sci. Technol. 12, no. 3 (2018): 199-205. Cited on 127.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “A new factor theorem for absolute matrix summability.” Quaest. Math. 42, no. 6 (2019): 803-809. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “Local properties of generalized absolute matrix summability of factored Fourier series.” Southeast Asian Bull. Math. 43, no. 2 (2019): 263-272. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “On the localization of factored Fourier series.” J. Comput. Anal. Appl. 29, no. 2 (2021): 344-354. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “A study on local properties of Fourier series.” Bol. Soc. Parana. Mat. (3) 39, no. 1 (2021): 201-211. Cited on 128.
Search in Google Scholar Back to article
Özarslan, Hikmet Seyhan. “Generalized absolute matrix summability of infinite series and Fourier series.” Indian J. Pure Appl. Math. 53, no. 4 (2022): 1083-1089. Cited on 128.
Search in Google Scholar Back to article

On absolute summability of infinite series and Fourier series

Abstract

Paradigm

My account