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

Published online by Cambridge University Press:  17 February 2009

C. E. M. Pearce  and
J. E. Pečarić
C. E. M. Pearce
Affiliation:
Department of Applied Mathematics, The University of Adelaide, South Australia 5005.
J. E. Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia.
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Abstract

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An improvement is made to two results of Brown and Shepp which are useful in calculations with fractal sets.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 1 , July 1994 , pp. 60 - 63
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Barnsley, M. F. and Demko, S., “Iterated function systems and the global construction of fractals”, Proc. Roy. Soc. London A 399 (1985) 243–275.Google Scholar
[2]Brown, G., “Some inequalities that arise in measure theory”, J. Austral. Math. Soc. Ser. A 45 (1988) 83–95.CrossRefGoogle Scholar
[3]Brown, G. and Shepp, L., “A convolution inequality”, in Contributions to Prob. and Stat. Essays in Honor of Ingram Olkin, (Springer, New York, 1989) 51–57.CrossRefGoogle Scholar
[4]Bullen, P. S., Mitrinović, D. S. and Vasić, P. M., Means and their inequalities (D. Reidel, Dordrecht, 1988).CrossRefGoogle Scholar
[5]Newhouse, S. E., “The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms”, Publ. Inst. des Hautes Etudes Scient. Publ. Math. 50 (1979) 101–151.CrossRefGoogle Scholar
[6]Palis, J. and Takens, F., “Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms”, Invent. Math. 82 (1985) 397–422.CrossRefGoogle Scholar