Geodesic
A new result on the quasi power increasing sequences
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 95-103.

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This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.
Keywords: almost increasing sequence, Hölder inequality, infinite series, Minkowski inequality, Riesz mean, quasi power increasing sequence, summability factor 
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Özarslan, Hikmet Seyhan. A new result on the quasi power increasing sequences. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 95-103. http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a7/

[1] Bari, Nina Karlovna, and Sergey B. Steckin. "Best approximations and differential properties of two conjugate functions." Trudy Moskov. Mat. Obšc. 5 (1956): 483-522.

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

[3] Bor, Hüseyin, and Lokenath Debnath. "Quasi β-power increasing sequences." Int. J. Math. Math. Sci. no. 41-44 (2004): 2371-2376.

[4] Flett, Thomas Muirhead. "On an extension of absolute summability and some theorems of Littlewood and Paley." Proc. London Math. Soc. (3) 7 (1957): 113-141.

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

[6] Leindler, László. "A new application of quasi power increasing sequences." Publ. Math. Debrecen 58, no. 4 (2001): 791-796.

[7] Maddox, Ivor John. Introductory Mathematical Analysis. Bristol: Adam Hilger Ltd., 1977.

[8] Mazhar, Syed Mohammad. "On |C, 1|k summability factors of infinite series." Indian J. Math. 14 (1972): 45-48.

[9] Mazhar, Syed Mohammad. "Absolute summability factors of infinite series." Kyungpook Math. J. 39, no. 1 (1999): 67-73.

[10] Ögdük, H. Nedret. "A summability factor theorem by using an almost increasing sequence." J. Comput. Anal. Appl. 11, no. 1 (2009): 45-53.

[11] Özarslan, Hikmet Seyhan, and Enes Yavuz. "A new note on absolute matrix summability." J. Inequal. Appl. (2013): Article 474.

[12] Özarslan, Hikmet Seyhan, and Aysegül Keten. "On a new application of almost increasing sequences." J. Inequal. Appl. (2013): Article 13.

[13] Özarslan, Hikmet Seyhan, and Enes Yavuz. "New theorems for absolute matrix summability factors." Gen. Math. Notes 23, no. 2 (2014): 63-70.

[14] Özarslan, Hikmet Seyhan. "On generalized absolute matrix summability methods." Int. J. Anal. Appl. 12, no. 1 (2016): 66-70.

[15] Özarslan, Hikmet Seyhan, and Ahmet Karakas. "A new result on the almost increasing sequences." J. Comput.Anal.Appl. 22, no. 6 (2017): 989-998.

[16] Özarslan, Hikmet Seyhan, and Bagdagül Kartal. "A generalization of a theorem of Bor." J. Inequal. Appl. (2017): Article 179.

[17] Özarslan, Hikmet Seyhan. "A new application of quasi power increasing sequences." AIP Conference Proceedings 1926, (2018): 1-6.

[18] Özarslan, Hikmet Seyhan. "A new factor theorem for absolute matrix summability." Quaest. Math. 42, no. 6 (2019): 803-809.

[19] Özarslan, Hikmet Seyhan. "Generalized quasi power increasing sequences." Appl. Math. E-Notes 19 (2019): 38-45.

[20] Özarslan, Hikmet Seyhan. "An application of absolute matrix summability using almost increasing and δ-quasi-monotone sequences." Kyungpook Math. J. 59, no. 2 (2019): 233-240.

[21] Sulaiman, Waadallah Tawfeeq. "Inclusion theorems for absolute matrix summability methods of an infinite series. IV." Indian J. Pure Appl. Math. 34, no. 11 (2003): 1547-1557.