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On two lemmas of Brown and Shepp having application to sum sets and fractals, II

Published online by Cambridge University Press:  17 February 2009

C. E. M. Pearce  and
J. Pečarić
C. E. M. Pearce
Affiliation:
Dept. of Applied Maths, The University of Adelaide, South Australia5005.
J. Pečarić
Affiliation:
Dept. of Applied Maths, The University of Adelaide, South Australia5005. Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
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Abstract

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Simple proofs are given of improved results of Brown and Shepp which are useful in calculations with fractal sets. A new inequality for convex functions is also obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 4 , April 1996 , pp. 490 - 494
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Brown, G. and Shepp, L., “A convolution inequality”, in Contributions to Prob. and Stat. Essays in Honor of Ingram Olkin1, (Springer, New York, 1989) 51–57.CrossRefGoogle Scholar
[2]Pearce, C. E. M. and Pečarić, J. E., “On two lemmas of Brown and Shepp having application to sum sets and fractals”, J. Austral. Math. Soc. Ser. B 36 (1994) 60–63.CrossRefGoogle Scholar
[3]Pearce, C. E. M. and Pečcarić, J. E., “An inequality for convex functions”, J. Math. Analysis and Applic. 183 (1994) 523–527.CrossRefGoogle Scholar
[4]Pečarić, J. E., “Generalization of the power means and their inequalities”, J. Math. Analysis and Applic. 161 (1991) 395–409.CrossRefGoogle Scholar
[5]Pečarić, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings and statistical applications (Academic Press, Boston, 1992).Google Scholar