Abstract

Let β>1. We define a class of similitudes S:=(fi(x)=xβni+ai:ni∈N+,ai∈R). Taking any finite collection of similitudes (fi(x))i=1m from S, it is well known that there is a unique self-similar set K1 satisfying K1=∪i=1mfi(K1). Similarly, another self-similar set K2 can be generated via the finite contractive maps of S. We call K1+K2=(x+y:x∈K1,y∈K2)
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