Generalised Riesz Typical Means

Jump To References Section

Authors

  • Jean Tzimbalario

Abstract

Definitions, notations and previous results. Let G{t) ≠ 0 be a continuous, positive, non-increasing function defined for t > 0 (if t < 0, set G{t) = 0), with G'(t)/G(t) non-decreasing and G(t) ∈ L(0, n) for every n > 0. Let λ = {λn} (n ≥ 0) be a strictly increasing unbounded sequence with λ0 ≥ 0 and let s = {sn} be an arbitrary sequence.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

1975-12-01

How to Cite

Tzimbalario, J. (1975). Generalised Riesz Typical Means. The Journal of the Indian Mathematical Society, 39(1-4), 83–101. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16638

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 Jean Tzimbalario

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

BORWEIN D. On the abscissa of summability of a Dirichlet series. J. London Math. Soc. 30 (1955), 68-71.

BOSANQUET L.S. Some extensions of M. Riesz's mean value theorem. Indian J. Math. 9 (1967), 65-90.

BOSANQUET L.S. Functional equation related to Riesz's mean value theorem. Publication of Ramanujan Institute 1 (1968), 47-69.

BOSANQUET L.S. An inequality for sequence transformations. Mathematika 13 (1966), 26-41.

HARDY G.H. AND RIESZ M. The general theory of Dirichlet's series. Cambridge Tracts No. 18; 1915, 1952.

JAKIMOVSKI A. AND TZIMBALARIO J. Inclusion relations for Riesz typical means. Proc. Cambridge Phil. Soc. 72 (1972), 417-423.

JAKIMOVSKI A. AND TZIMBALARIO J. Inclusion relations for general Riesz typical means. Canad. Math. Bull. 17(1974), 51-61.

JAKIMOVSKI A. AND TZIMBALARIO J. Inclusion relations for absolute Riesz typical means and a conjecture by Maddox. 30(1975) 366-384.

JURKATNV.B. uber Konvergenzfaktoren bei Rieszschen Mitteln. Math. Zeit. 54 (1951), 262-271.

JURKAT W.B. Ober Rieszsche Mitteln mit unstetigem Parameter. Math. Zeit. 55 (1951), 8-12.

MADDOX I.J. Some inclusion theoroms. Proc. Glasgow Math. Ass. 6(1964) 161-168.

MADDOX I.J. Convergence and summability factors for Riesz means. Proc. London Math. Soc. 12 (1962), 345-366.

PEYERIMHOFF A. Konvergenz und Summierbarkeitsfaktoren. Math. Zeit. 55 (1951) 23-54.

RUSSELL D.C. Summability methods which include the Riesz typical means. Proc. Cambridge Phil. Soc. 69 (1971), 99-106 and 297-300.

WILANSKY A. AND ZELLER K. Abschnittsbeschrankte Matrixtransformationen; starke Limitierbarkeit Math. Zeit. 64 (1956), 258-269.

WILANSKY A. Functional Analysis. Blaisdell (1964).

ZELLER K. AND BEEKMANN W. Theorie der Limitierungsverfahrungen. SpringerVerlag, Berlin 1970.