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A matrix application on absolute weighted arithmetic mean summability factors of infinite series. (English) Zbl 1440.40005

A result of H. Bor [Int. J. Anal. Appl. 14, No. 2, 175–179 (2017; Zbl 1384.40004)] regarding \(\left\vert A;\theta _{n}\right\vert _{k}\) summability of infinite series is generalized and improved by application of almost increasing sequences in place of positive non-decreasing ones. Also, some new and known results are obtained as corollaries.

MSC:

40D15 Convergence factors and summability factors
26D15 Inequalities for sums, series and integrals
40F05 Absolute and strong summability
40G99 Special methods of summability
42A24 Summability and absolute summability of Fourier and trigonometric series
46A45 Sequence spaces (including Köthe sequence spaces)

Citations:

Zbl 1384.40004
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References:

[1] N.K.Bari and S.B. Stechkin, Best approximation and differential properties of two conjugate functions, Tr. Mosk. Mat. Obshch., vol. 5 (1956), 483-522.
[2] H. Bor, On two summability methods, Math. Proc. Camb. Philos. Soc., 97 (1985), 147-149. · Zbl 0554.40008
[3] H. Bor, A note on \(|\bar{N}, p_n|_k\) summability factors of infinite series, Indian J. Pure Appl. Math., 18 (1987), 330-336. · Zbl 0631.40004
[4] H. Bor, Factors for absolute weighted arithmetic mean summability of infinite series, Int. J. Anal. and Appl., 14 (2) (2017), 175-179. · Zbl 1384.40004
[5] E. Cesàro, Sur la multiplication des séries, Bull. Sci. Math., 14 (1890), 114-120. · JFM 22.0248.01
[6] T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. Lond. Math. Soc., 7 (1957), 113-141. · Zbl 0109.04402
[7] G. H. Hardy, Divergent Series, Clarendon Press, Oxford (1949). · Zbl 0032.05801
[8] K. N. Mishra, On the absolute Nörlund summability factors of infinite series, Indian J. Pure Appl. Math., 14 (1983), 40-43. · Zbl 0525.40006
[9] K. N. Mishra and R. S. L. Srivastava, On the absolute Cesaro summability factors of infinite series, Portugal Math., 42 (1983/84), 53-61. · Zbl 0597.40003
[10] K. N. Mishra and R. S. L. Srivastava, On \(|\bar{N}, p_n|\) summability factors of infinite series, Indian J. Pure Appl. Math.,15 (1984), 651-656. · Zbl 0571.40008
[11] W., T. Sulaiman, Inclusion theorems for absolute matrix summability methods of an infinite series, IV. Indian J. Pure Appl. Math. 34 11 (2003), 1547-1557. · Zbl 1039.40003
[12] N. Tanovi \(\breve{c} \)-Miller, On strong summability, Glas. Mat. Ser III 14 (34) (1979), 87-97.
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