A new theorem on generalized absolute Cesàro summability factors. (English) Zbl 1499.40065
Summary: In this paper, we have proved a new theorem dealing with \(\varphi - |C, \alpha|_k\) summability factors of infinite series under weaker conditions. Also, some new and known results are obtained.
MSC:
| 40D15 | Convergence factors and summability factors |
| 26D15 | Inequalities for sums, series and integrals |
| 40F05 | Absolute and strong summability |
| 40G05 | Cesàro, Euler, Nörlund and Hausdorff methods |
Keywords:
Cesàro mean; absolute summability; almost increasing sequence; quasi-\(\sigma \)-power increasing sequence; infinite series; Hölder’s inequality; Minkowski’s inequalityReferences:
| [1] | M. Balci, Absolute \(\varphi \)-summability factors, Comm. Fac. Sci. Univ. Ankara, Ser. A1 29 (1980), 63-68. · Zbl 0498.40004 |
| [2] | N.K. Bari and S.B. Steckin, Best approximation and differential properties of two conjugate functions, Trudy. Moskov. Mat. Obsc. 5 (1956), 483-522. · Zbl 0072.05702 |
| [3] | H. Bor, Factors for generalized absolute Cesaro summability methods, Publ. Math. Debrecen 43 (1993), 297-302. · Zbl 0797.40004 |
| [4] | H. Bor, A new study on generalized absolute Cesaro summability methods, Quaest. Math. 43 (2020), (in press). · Zbl 1468.40004 |
| [5] | L.S. Bosanquet, A mean value theorem, J. London Math. Soc. 16 (1941), 146-148. · Zbl 0028.21901 · doi:10.1112/jlms/s1-16.3.146 |
| [6] | E. Cesaro, Sur la multiplication des series, Bull. Sci. Math. 14 (1890), 114-120. · JFM 22.0248.01 |
| [7] | T.M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. 7 (1957), 113-141. · Zbl 0109.04402 |
| [8] | T.M. Flett, Some more theorems concerning the absolute summability of Fourier series, Proc. London Math. Soc. 8 (1958), 357-387. · Zbl 0109.04502 |
| [9] | E. Kogbetliantz, Sur les series absolument sommables par la methode des moyennes arithmetiques, Bull. Sci. Math. 49 (1925), 234-256. · JFM 51.0182.01 |
| [10] | L. Leindler, A new application of quasi power increasing sequences, Publ. Math. Debrecen 58 (2001), 791-796. · Zbl 0980.40004 |
| [11] | S.M. Mazhar, Absolute summability factors of infinite series, Kyungpook Math. J. 39 (1999), 67-73. · Zbl 0932.40006 |
| [12] | T. · Zbl 0057.30002 · doi:10.1215/S0012-7094-54-02127-4 |
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