Iteration of random-valued functions on the unit interval

On a Refinement Type Equation

“…This definition of iterates were introduced independently in [3] and [14], and then studied also in [1], [17] and [20]. It turns out that such iterates are useful for instance in solving functional equations (see [2], [16], [18]).…”

“…Since ϕ is measurable with respect to B(R) ⊗ A, it follows that its iterates are measurable with respect to B(R) ⊗ A ∞ (see [3]). Thus we can iterate inequality (3.4).…”

Convergence of sequences of iterates of random-valued vector functions

“…These iterates were defined independently in [4] and [7]. In [4] and [9] some conditions are established which guarantee the convergence (a.s. and in L 1 ) of ð f n ðx; ÁÞÞ. Fix a random-valued function f : X Â !…”

Sequences of iterates of random-valued vector functions and continuous solutions of related equations

“…However it may happen that instead of the exact value of a function at a point we know only some parameters of this value. The iterates of such functions were defined independently by K. Baron and M. Kuczma [4] and Ph. Diamond [5].…”