New results for almost increasing sequences

Bağdagül Kartal

Abstract


In the present paper, two theorems of absolute summability have been proved by using the definition of almost increasing sequence.

Keywords


almost increasing sequences; Holder inequality; infinite series; Minkowski inequality; Riesz mean; summability factor

Mathematics Subject Classification (2010)


26D15; 40D15; 40F05; 40G99

References


Bari, N.K. and S.B. Steˇckin. "Best approximations and differential properties of two conjugate functions." Trudy Moskov. Mat. Obsc. 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, 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.

Mazhar, Syed Mohammad. "A note on absolute summability factors." Bull. Inst. Math. Acad. Sinica 25, no. 3 (1997): 233-242.

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.


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