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On applications of quasi-monotone sequences and quasi power increasing sequences. (English) Zbl 1427.40005

Summary: In this article, we prove a general theorem dealing with an application of quasi-\(f\)-power increasing sequences and \(\delta\)-quasi monotone sequences. This theorem also includes some known and new results.

MSC:

40D15 Convergence factors and summability factors
40F05 Absolute and strong summability
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
Full Text: DOI

References:

[1] Bari, N. K.; Stečkin, S. B., Best approximation and differential properties of two conjugate functions, Trudy Moskov. Mat. Obshch, 5, 483-522 (1956) · Zbl 0072.05702
[2] Boas, R. P., Quasi-positive sequences and trigonometric series, Proc. Lond. Math. Soc. Ser. A, 14, 38-46 (1965) · Zbl 0128.29302 · doi:10.1112/plms/s3-14A.1.38
[3] Sulaiman, W. T., Extension on absolute summability factors of infinite series, J. Math. Anal. Appl, 322, 2, 1224-1230 (2006) · Zbl 1100.40005 · doi:10.1016/j.jmaa.2005.09.019
[4] Leindler, L., A new application of quasi power increasing sequences, Publ. Math. Debrecen, 58, 791-796 (2001) · Zbl 0980.40004
[5] Borwein, D., Theorems on some methods of summability, Q. J. Math, 9, 1, 310-316 (1958) · Zbl 0084.05901 · doi:10.1093/qmath/9.1.310
[6] Bor, H., On a new application of quasi power increasing sequences, Proc. Estonian Acad. Sci, 57, 4, 205-209 (2008) · Zbl 1221.40006 · doi:10.3176/proc.2008.4.01
[7] Bor, H., A newer application of almost increasing sequences, Pac. J. Appl. Math, 2, 211-216 (2010) · Zbl 1352.40005
[8] Das, G. A., Tauberian theorem for absolute summability, Proc. Camb. Philos. Soc, 67, 32-326 (1970) · Zbl 0205.07901
[9] Bor, H., An application of almost increasing sequences, Appl. Math. Lett, 24, 3, 298-301 (2011) · Zbl 1216.40005 · doi:10.1016/j.aml.2010.10.009
[10] Balcı, M., Absolute \(####\)-summability factors, Commun. Fac. Sci. Univ. Ankara Ser. A1, 29, 63-68 (1980) · Zbl 0498.40004
[11] Flett, T. M., On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc, 7, 113-141 (1957) · Zbl 0109.04402 · doi:10.1112/plms/s3-7.1.113
[12] Flett, T. M., Some more theorems concerning the absolute summability of Fourier series, Proc. Lond. Math. Soc, 8, 357-387 (1958) · Zbl 0109.04502 · doi:10.1112/plms/s3-8.3.357
[13] Bor, H.; Yu, D. S., A new application of almost increasing and quasi-monotone sequences, Appl. Math. Lett, 24, 8, 1347-1350 (2011) · Zbl 1221.40008 · doi:10.1016/j.aml.2011.03.006
[14] Bor, H., On the quasi monotone and generalized power increasing sequences and their new applications, J. Class. Anal, 2, 139-144 (2013) · Zbl 1412.26042 · doi:10.7153/jca-02-11
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