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Inequalities for certain cyclic sums II

Published online by Cambridge University Press:  20 January 2009

J. C. Boarder  and
D. E. Daykin
J. C. Boarder
Affiliation:
University of Reading, Berkshire
D. E. Daykin
Affiliation:
University of Reading, Berkshire
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Let k ≧ 2 be an integer and each of ν1, ν2, …, νk and δ1, δ2, …, δk be 0 or 1. Then given any positive integer M and non-negative reals a1, a2, …, aM we put

where

and

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 3 , June 1973 , pp. 209 - 218
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

REFERENCES

(1) Boarder, J. C., M.Phil. Thesis, University of Reading, (1972).Google Scholar
(2) Daykin, D. E., Inequalities for functions of a cyclic nature, J. London Math. Soc. (2) 3 (1971), 453–462.CrossRefGoogle Scholar
(3) Daykin, D. E., Inequalities for certain cyclic sums, Proc. Edinburgh Math. Soc. (2) 17 (1971), 257–262.CrossRefGoogle Scholar
(4) Diananda, P. H., Extensions of an inequality of H. S. Shapiro, Amer. Math. Monthly, 66 (1959), 489–491.Google Scholar
(5) Nowosad, P., Isoperimetric eigenvalue problems in algebra, Comm. Pure Appl Math. 21 (1968), 401–465.CrossRefGoogle Scholar