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Theorem 4 (Iacus and La Torre, 2001)

Under conditions i) to v):

**1.** T_{p} is an operator from

to itself.

**2.** Suppose that w_{i}(x) = x, P _{i} = p, and δ_{i} ≥ −p, then

**3.**

then *T _{p}* is a contraction on

with contractivity

constant c.

**4.** Let

such that T_{p}F_{1} = F_{1} and T_{p}* F_{2} = F_{2}. Then

where c is the contractivity constant of T_{p}. The theorem above assures the IFS nature of the operator T_{p} that can be denoted, as in the previous section, as a N-maps IFS(w, p) with obvious notation. The goal is again the solution of the inverse problem in terms of p. Consider the following convex set:

then we have the following results:

... in Theorem 5

Stefano M. Iacus, Davide La Torre

**Next: ** Theorem 5 (Iacus and La Torre, 2001).

**Summary: **Index