Asymptotic order of the quantization error for a class of self-similar measures with overlaps

Let \fᵢ\₈=₁N be a set of equi-contractive similitudes on R¹ satisfying the finite-type condition. We study the asymptotic quantization error for self-similar measures associated with \fᵢ\₈=₁N and a positive probability vector. With a verifiable assumption, we prove that the upper and lower quantization coefficient for are both bounded away from zero and infinity. This can be regarded as an extension of Graf and Luschgy's result on self-similar measures with the open set condition. Our result is applicable to a significant class of self-similar measures with overlaps, including Erd\"os measure, the 3-fold convolution of the classical Cantor measure and the self-similar measures on some -Cantor sets.