## Upper convex density and similarly contractive fixed points## Jiandong Yin, Zuoling Zhou
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 Hausdorff measure and on topological entropy: A brief
survey of recent results, Nonlinearity 17(2004), 493-502].
Tbilisi Mathematical Journal, Vol. 5(1) (2012), pp. 39-49 |