Generalized absolute Cesàro summability of factored infinite series. (English) Zbl 1524.40030
Summary: In this paper, we have proved a general theorem dealing with \(\varphi\)-\(|C, \alpha, \beta|_k\) summability factors of infinite series. Also, we have obtained some new and known results related to the different special summability methods.
MSC:
| 40G05 | Cesàro, Euler, Nörlund and Hausdorff methods |
| 26D15 | Inequalities for sums, series and integrals |
| 40D15 | Convergence factors and summability factors |
| 40F05 | Absolute and strong summability |
Keywords:
Cesàro mean; absolute summability; infinite series; Hölder’s inequality; Minkowski’s inequalityReferences:
| [1] | M. Balcı, Absolute φ-summability factors, Comm. Fac. Sci. Univ. Ankara, Ser. A 1 29 (1980), 63-68. · Zbl 0498.40004 |
| [2] | H. Bor, Factors for generalized absolute Cesàro summability methods, Publ. Math. Debre-cen 43 (1993), 297-302. · Zbl 0797.40004 |
| [3] | H. Bor, On a new application of quasi power increasing sequences, Proc. Est. Acad. Sci. 57 (2008), 205-209. · Zbl 1221.40006 |
| [4] | H. Bor, A newer application of almost increasing equences, Pac. J. Appl. Math. 2 (2010), 211-216. · Zbl 1352.40005 |
| [5] | H. Bor, An application of almost increasing sequence, Appl. Math. Lett. 24 (2011), 298-301. · Zbl 1216.40005 |
| [6] | D. Borwein, Theorems on some methods of summability, Quart. J. Math. Oxford Ser. 2 9 (1958), 310-316. · Zbl 0084.05901 |
| [7] | G. Das, A Tauberian theorem for absolute summability, Proc. Camb. Phil. Soc. 67 (1970), 32-326. · Zbl 0205.07901 |
| [8] | 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 |
| [9] | T.M. Flett, Some more theorems concerning the absolute summability of Fourier series, Proc. London Math. Soc. 8 (1958), 357-387. · Zbl 0109.04502 |
| [10] | K.N. Mishra and R.S.L. Srivastava, On absolute Cesàro summability factors of infinite series, Portugal. Math. 42 (1983-1984), 53-61. · Zbl 0597.40003 |
| [11] | T. Pati, The summability factors of infinite series, Duke Math. J. 21 (1954), 271-284. · Zbl 0057.30002 |
| [12] | Hüseyin Bor received his Ph.D. degree from Department of Mathematics, Ankara Uni-versity in 1982 and he retired from Erciyes University in 2011. He is currently an Emeritus Professor and he is an independent researcher in Ankara. His research interests include sequences, series, summability, and Fourier Analysis. He is the author of 250 research pa-pers published in the reputed international mathematics journals. He also serves as referee and editor in many mathematical journals. |
| [13] | P.O. Box 121, TR-06502 Bahçelievler, Ankara, Turkey e-mail: hbor33@gmail.com |
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