Geodesic
An application of almost increasing sequences
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 16-20.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a general theorem on absolute Cesàro summability of an infinite series is proved by using an almost increasing sequence instead of a positive non-decreasing sequence.
Keywords: almost increasing sequences, Cesàro summability, Hölder's inequality, infinite series, Minkowski's inequality, summability factor. 
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B. Kartal. An application of almost increasing sequences. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 16-20. http://geodesic.mathdoc.fr/item/IVM_2021_11_a1/

[1] Cesàro E., “Sur la multiplication des séries”, Bull. Sci. Math., 14 (1890), 114–120

[2] Pati T., “The summability factors of infinite series”, Duke Math. J., 21 (1954), 271–283 | DOI | Zbl

[3] Seyhan H., “On the generalized Cesàro summability factors”, Acta Comment. Univ. Tartu. Math., 3 (1999), 3–6 | Zbl

[4] Flett T. M., “Some more theorems concerning the absolute summability of Fourier series and power series”, Proc. London Math. Soc. (3), 8 (1958), 357–387 | DOI | Zbl

[5] Flett T. M., “On an extension of absolute summability and some theorems of Littlewood and Paley”, Proc. London Math. Soc. (3), 7 (1957), 113–141 | DOI | Zbl

[6] Bor H., “On the absolute Cesàro summability factors”, Anal. Numér. Théor. Approx., 20:1–2 (1991), 11–14 | Zbl

[7] Bor H., Özarslan H. S., “A note on absolute summability factors”, Adv. Stud. Contemp. Math., 6:1 (2003), 1–11

[8] Bor H., Seyhan H., “A note on almost increasing sequences”, Comment. Math. Prace Mat., 39 (1999), 37–42 | Zbl

[9] Özarslan H. S., “On the generalized Cesàro summability factors”, Acta Math. Acad. Paedagog. Nyházi, 17:1 (2001), 3–7 | Zbl

[10] Özarslan H. S., “Factors for the $\varphi-\left|C,\alpha \right|_{k}$ summability”, Adv. Stud. Contemp. Math., 5:1 (2002), 25–31 | Zbl

[11] Özarslan H. S., “A note on absolute summability factors”, Proc. Indian Acad. Sci. Math. Sci., 113:2 (2003), 165–169 | DOI | Zbl

[12] Özarslan H. S., “Absolute Cesàro summability factors”, J. Concr. Appl. Math., 5:3 (2007), 231–236 | Zbl

[13] Özarslan H. S., “On absolute Cesàro summability factors of infinite series”, Commun. Math. Anal., 3:1 (2007), 53–56 | Zbl

[14] Özarslan H. S., “A note on generalized absolute Cesàro summability”, J. Comp. Anal. Appl., 12:3 (2010), 581–585 | Zbl

[15] Seyhan H., “A note on summability methods”, Math. Slovaca, 49:2 (1999), 201–208 | Zbl

[16] Bari N. K. Stečkin S. B., “Best approximations and differential properties of two conjugate functions”, Trudy Moskov. Mat. Obšč., 5, 1956, 483–522 (in Russian) | Zbl

[17] Bosanquet L. S., “A mean value theorem”, J. London Math. Soc., 16 (1941), 146–148 | DOI

[18] Mazhar S. M., “A note on absolute summability factors”, Bull. Inst. Math. Acad. Sinica, 25 (1997), 233–242 | Zbl