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Existence of fixed point of a Frobenius-Perron type operator  P  :  L  1  ⟶  L  1  generated by a family { φ y  }  y ∈ Y   of nonsingular Markov maps defined on a  σ -finite measure space ( I ,  Σ ,  m ) is studied. Two fairly general conditions are established and it is proved that they imply for any  g  ∈  G  = { f  ∈  L  1  :  f  ≥ 0, and ∥ f ∥ = 1}, the convergence (in the norm of  L  1 ) of the sequence{   P   j    g   }   j  =  1    ∞$\begin{array}{} \{P^{j}g\}_{j = 1}^{\infty} \end{array} $    to a unique fixed point  g  0 . The general result is applied to a family of  C  1+ α  -smooth Markov maps in ℝ  d  .

Fixed point of some Markov operator of Frobenius-Perron type generated by a random family of point-transformations in ℝ d