Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T07:52:52.841Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ,
M. Matić ,
C. E. M. Pearce  and
J. Pečarić
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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
The ANZIAM Journal , Volume 41 , Issue 3 , January 2000 , pp. 329 - 337
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Alzer, H., “Comments on some inequalities of Pearce and Pečarić”, Proc. Edin. Math. Soc. 40 (1997) 167–174.CrossRefGoogle Scholar
[2]Brown, G., “Inequalities for measures of sum sets”, Proc. CMA ANU 15 (1987) 15–20.Google Scholar
[3]Brown, G., “Some inequalities that arise in measure theory”, J. Austral. Math. Soc. Ser. B 45 (1988) 83–94.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) 87–94.CrossRefGoogle Scholar
[5]Brown, G. and Moran, W., “Raikov systems and radicals in convolution measure algebras”, J. London Math. Soc. 28 (1983) 531–542.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) 25–46.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) 51–57.CrossRefGoogle Scholar
[8]Brown, G. and Williamson, J. H., “Coin tossing and sum sets”, J. Austral. Math. Soc. Ser. A 43 (1987) 211–219.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) 17–22.Google Scholar
[10]Hajela, D. and Seymour, P., “Counting points in hypercubes and convolution measure algebras”, Combinatorica 5 (1985) 205–214.CrossRefGoogle Scholar
[11]Kemp, A. W., “Certain inequalities involving fractional powers”, J. Austral. Math. Soc. Ser. A 53 (1992) 131–136.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) 337–392.CrossRefGoogle Scholar
[13]Oberlin, D. M., “The size of sums of sets II”, Israel J. Math. 55 (1986) 305–316.CrossRefGoogle Scholar
[14]Pearce, C. E. M. and Pečarić, J. E., “An inequality for convex functions”, J. Math. Anal. Appl. 183 (1994) 523–527.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) 60–63.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) 208–211.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) 490–494.CrossRefGoogle Scholar
[18]Pittenger, A. O., “Inequalities between symmetric, logarithmic and power means”, Univ. Beograd Publ. Elektrotechn. Fak. Ser. Mat. Fiz. 678–715 (1980) 19–21.Google Scholar
[19]Woodall, D. R., “A theorem on cubes”, Mathematika 24 (1977) 60–62.CrossRefGoogle Scholar