### A new application of almost increasing sequences

#### Abstract

*N*

*, p*|

_{n}*summability of infinite series has been generalized to the φ-|*

_{k}*N*

*, p*δ|

_{n};*infinite series by using an almost increasing sequence.*

_{k}#### Keywords

#### Mathematics Subject Classification (2010)

#### References

Bari, N.K. and S.B. Steckin. "Best approximations and differential properties of two conjugate functions." Trudy Moskov. Mat. Obšc. 5 (1956): 483-522.

Bor, Hüseyin. "On two summability methods." Math. Proc. Cambridge Philos. Soc. 97, no. 1 (1985): 147-149.

Bor, Hüseyin. "On local property of |N, pn|k summability of factored Fourier series." J. Math. Anal. Appl. 179, no. 2 (1993): 646-649.

Bor, Hüseyin and Hikmet Seyhan. "On almost increasing sequences and its applications." Indian J. Pure Appl. Math. 30, no. 10 (1999): 1041-1046.

Bor, Hüseyin, and Hikmet S. Özarslan. "On absolute Riesz summability factors." J. Math. Anal. Appl. 246, no. 2 (2000): 657-663.

Bor, Hüseyin. "On absolute Riesz summability factors." Adv. Stud. Contemp. Math. (Pusan) 3, no. 2 (2001): 23-29.

Bor, Hüseyin, and Hikmet S. Özarslan. "A note on absolute summability factors." Adv. Stud. Contemp. Math. (Kyungshang) 6, no. 1 (2003): 1-11.

Hardy, Godfrey Harold. Divergent Series. Oxford: Oxford University Press, 1949.

Karakas, Ahmet. "A note on absolute summability method involving almost increasing and -quasi-monotone sequences." Int. J. Math. Comput. Sci. 13, no. 1 (2018): 73-81.

Kartal, Bagdagül. "On generalized absolute Riesz summability method." Commun. Math. Appl. 8, no. 3 (2017): 359-364.

Özarslan, Hikmet S. "On almost increasing sequences and its applications." Int. J. Math. Math. Sci. 25, no. 5 (2001): 293-298.

Özarslan, Hikmet S. "A note on |N, pn|k summability factors." Indian J. Pure Appl. Math. 33, no. 3 (2002): 361-366.

Özarslan, Hikmet S. "On |N, pn|k summability factors." Kyungpook Math. J. 43, no. 1 (2003): 107-112.

Seyhan, Hikmet. "On the local property of φ-|N, pn;δ|k summability of factored Fourier series." Bull. Inst. Math. Acad. Sinica 25, no. 4 (1997): 311-316.

Seyhan, Hikmet, and Abdulcabbar Sönmez, "On φ-|N, pn;δ|k summability factors." Portugal. Math. 54, no. 4 (1997): 393-398.

Seyhan, Hikmet. "A note on absolute summability factors." Far East J. Math. Sci. 6, no. 1 (1998): 157-162.

Seyhan, Hikmet. "On the absolute summability factors of type (A,B)." Tamkang J. Math. 30, no. 1 (1999): 59-62.

Download statistics: 924

This article by

*Ahmet Karakaş*is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN

*775/P-DUN/2017*see more

The Journal is indexed in:

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019