A generalization of strong Rieszian summability
HTML articles powered by AMS MathViewer
- by L. I. Holder PDF
- Proc. Amer. Math. Soc. 42 (1974), 452-460 Request permission
Abstract:
Strong summability, $[\alpha ,\beta ;p]$, for the Bosanquet-Linfoot $(\alpha ,\beta )$ summability method is defined so that $[\alpha ,0;p]$ is identical to strong Rieszian summability, $[R;\alpha ,p]$. The main result proved in this paper shows consistency in the sense that $[\alpha ,\beta ;p]$ summability implies $[\alpha ’,\beta ’;q]$ summability, for $\alpha ’ > \alpha$ or $\alpha ’ = \alpha ,\beta ’ > \beta$; and $1 \leqq q \leqq p$. Also, a necessary condition for $[\alpha ,\beta ;p]$ summability and relationships between strong and absolute $(\alpha ,\beta )$ summability are given.References
-
L. S. Bosanquet and E. H. Linfoot, Generalized means and the summability of Fourier series, Quart. J. Math. Oxford Ser. 2 (1931), 207-229.
- A. V. Boyd and J. M. Hyslop, A definition for strong Rieszian summability and its relationship to strong Cesàro summability, Proc. Glasgow Math. Assoc. 1 (1952), 94–99. MR 51330
- B. J. Boyer and L. I. Holder, A generalization of absolute Rieszian summability, Proc. Amer. Math. Soc. 14 (1963), 459–464. MR 149155, DOI 10.1090/S0002-9939-1963-0149155-4
- J. M. Hyslop, Note on the strong summability of series, Proc. Glasgow Math. Assoc. 1 (1952), 16–20. MR 50693
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 452-460
- MSC: Primary 40F05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0348328-2
- MathSciNet review: 0348328