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

Published online by Cambridge University Press:  17 February 2009

N. Elezović
Affiliation:
Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
M. Matić
Affiliation:
Department of Mathematics, FESB, R. Boškovića B.B., 21 000 Split, Croatia
C. E. M. Pearce
Affiliation:
Department of Applied Mathematics, The University of Adelaide, SA 5005, Australia
J. Pečarić
Affiliation:
Department of Applied Mathematics, The University of Adelaide, SA 5005, Australia
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Abstract

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We improve some results of [17], which relate to key tools given in [7] for establishing canonical inequalities used in the analysis of sum sets and fractals.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Alzer, H., “Comments on some inequalities of Pearce and Pečarić”, Proc. Edin. Math. Soc. 40 (1997) 167174.CrossRefGoogle Scholar
[2]Brown, G., “Inequalities for measures of sum sets”, Proc. CMA ANU 15 (1987) 1520.Google Scholar
[3]Brown, G., “Some inequalities that arise in measure theory”, J. Austral. Math. Soc. Ser. B 45 (1988) 8394.CrossRefGoogle Scholar
[4]Brown, G., Keane, M. S., Moran, W. and Pearce, C. E. M., “An inequality with applications to Cantor measure and normal numbers”, Mathematika 35 (1988) 8794.CrossRefGoogle Scholar
[5]Brown, G. and Moran, W., “Raikov systems and radicals in convolution measure algebras”, J. London Math. Soc. 28 (1983) 531542.CrossRefGoogle Scholar
[6]Brown, G., Pearce, C. E. M., Pečarić, J. and Yin, Q., “Measures of algebraic sums of sets”. Math. Ineq. and Applic. 2 (1999) 2546.Google Scholar
[7]Brown, G. and Shepp, L. A., “A convolution inequality”, in Contributions to probability and statistics, Essays in honor of Ingram Olkin, (Springer, N. Y., 1989) 5157.CrossRefGoogle Scholar
[8]Brown, G. and Williamson, J. H., “Coin tossing and sum sets”, J. Austral. Math. Soc. Ser. A 43 (1987) 211219.CrossRefGoogle Scholar
[9]Brown, G. and Yin, Q., “Some metric properties of sum sets”, in Number theory with an emphasis on the Markoff spectrum, Lecture Notes in Pure and Applied Mathematics 147 (1993) 1722.Google Scholar
[10]Hajela, D. and Seymour, P., “Counting points in hypercubes and convolution measure algebras”, Combinatorica 5 (1985) 205214.CrossRefGoogle Scholar
[11]Kemp, A. W., “Certain inequalities involving fractional powers”, J. Austral. Math. Soc. Ser. A 53 (1992) 131136.CrossRefGoogle Scholar
[12]Landau, H. T., Logan, B. F. and Shepp, L. A., “An inequality conjectured by Hajela and Seymour arising in combinational geometry”, Combinatorica 5 (1985) 337392.CrossRefGoogle Scholar
[13]Oberlin, D. M., “The size of sums of sets II”, Israel J. Math. 55 (1986) 305316.CrossRefGoogle Scholar
[14]Pearce, C. E. M. and Pečarić, J. E., “An inequality for convex functions”, J. Math. Anal. Appl. 183 (1994) 523527.CrossRefGoogle Scholar
[15]Pearce, C. E. M. and Pečarić, J. E., “On two lemmas of Brown and Shepp having applications to sum sets and fractals”, J. Austral. Math. Soc. Ser. B 36 (1994) 6063.CrossRefGoogle Scholar
[16]Pearce, C. E. M. and Pečarić, J. E., “On an inequality relating to sum sets”, J. Austral. Math. Soc. Ser. B 37 (1995) 208211.CrossRefGoogle Scholar
[17]Pearce, C. E. M. and Pečarić, J. E., “On two lemmas of Brown and Shepp having applications to sum sets and fractals II”, J. Austral. Math. Soc. Ser. B 37 (1996) 490494.CrossRefGoogle Scholar
[18]Pittenger, A. O., “Inequalities between symmetric, logarithmic and power means”, Univ. Beograd Publ. Elektrotechn. Fak. Ser. Mat. Fiz. 678–715 (1980) 1921.Google Scholar
[19]Woodall, D. R., “A theorem on cubes”, Mathematika 24 (1977) 6062.CrossRefGoogle Scholar