An imp ortant interpretation of the contraction mapping theorem is thefollowing. Assume that the function f(x, θ) satisfies the condition of the theorem then, for each θ∗ ∈ Ω the equation f(x, θ∗) − x = 0 has a solution in xand moreover it is unique. To illustrate this idea consider the function h(x, θ)defined as
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