Box Dimensions Of Inhomogeneous Self-similar Sets

This paper is a report on the lasted literature about the box dimensions of inhomo-geneous self-similar sets.Firstly,we provide an estimate for the upper box dimension of the inhomogeneous self-similar sets and prove that the upper box dimension satisfies the finite stable property providing certain separation conditions assumed.Secondly,for the lower box dimension,we point out that the finite stable property could not always hold,but we will provide some sufficient conditions which can ensure it holds.