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2012 Upper convex density and similarly contractive fixed points
Jiandong Yin, Zuoling Zhou
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Tbilisi Math. J. 5(1): 39-49 (2012). DOI: 10.32513/tbilisi/1528768888


In this work, for the self similar sets satisfying the open set condition, we obtain an interesting character that the upper convex density at every similarly contractive fixed point equalling 1 implies that the upper convex densities at all the points are equal to 1. By using this result, we sufficiently answer the open problem 6 posed by Z. Zhou and L. Feng in [Twelve open problems on the exact value of the Hausdor measure and on topological entropy: A brief survey of recent results, Nonlinearity, 17(2004) 493–502.].


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Jiandong Yin. Zuoling Zhou. "Upper convex density and similarly contractive fixed points." Tbilisi Math. J. 5 (1) 39 - 49, 2012.


Received: 8 October 2011; Revised: 30 June 2012; Accepted: 10 July 2012; Published: 2012
First available in Project Euclid: 12 June 2018

zbMATH: 1281.28001
MathSciNet: MR2969979
Digital Object Identifier: 10.32513/tbilisi/1528768888

Primary: 28A78
Secondary: 28A80

Rights: Copyright © 2012 Tbilisi Centre for Mathematical Sciences


Vol.5 • No. 1 • 2012
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