A Tauberian theorem for strong Abel summability type
HTML articles powered by AMS MathViewer
- by Indulata Sukla PDF
- Proc. Amer. Math. Soc. 84 (1982), 185-191 Request permission
Abstract:
In the present paper the author has defined a new method of strong Abel summability type ${\{ A,\lambda \} _m}$ and obtained a necessary and sufficient type of Tauberian conditions for $\Sigma {a_n}$ to be summable ${[R,\lambda ,k]_m}$, whenever it is summable ${\{ A,\lambda \} _m}$. This result is analogous to one result of Flett [4].References
- 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
- K. Chandrasekharan and S. Minakshisundaram, Typical means, Oxford University Press, 1952. MR 0055458
- T. M. Flett, Some generalizations of Tauber’s second theorem, Quart. J. Math. Oxford Ser. (2) 10 (1959), 70–80. MR 130510, DOI 10.1093/qmath/10.1.70
- T. M. Flett, Some remarks on strong summability, Quart. J. Math. Oxford Ser. (2) 10 (1959), 115–139. MR 107769, DOI 10.1093/qmath/10.1.115
- Martin Glatfeld, On strong Rieszian summability, Proc. Glasgow Math. Assoc. 3 (1957), 123–131. MR 118992
- G. H. Hardy and M. Riesz, The general theory of Dirichlet’s series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 18, Stechert-Hafner, Inc., New York, 1964. MR 0185094
- Pramila Srivastava, On strong Rieszian summability of infinite series, Proc. Nat. Inst. Sci. India Part A 23 (1957), 58–71. MR 96057
- Pramila Srivastava, On strong summability of infinite series, Math. Student 31 (1963), 187–192 (1964). MR 177231
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 185-191
- MSC: Primary 40E05; Secondary 40G10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637166-3
- MathSciNet review: 637166