Fractal dimensions of fractal transformations and quantization dimensions for bi-Lipschitz mappings

Abstract

In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the quantization dimension of the invariant measure corresponding to a weighted iterated function system consisting of bi-Lipschitz mappings under the strong open set condition.