Glasnik Matematicki, Vol. 42, No.2 (2007), 389-399.

SEQUENCES OF ITERATES OF RANDOM-VALUED VECTOR FUNCTIONS AND CONTINUOUS SOLUTIONS OF RELATED EQUATIONS

Rafal Kapica

Abstract.   Given a probability space (Ω, A, P), a separable metric space X, and a random-valued vector function f : X × Ω → X, we obtain some theorems on the existence and on the uniqueness of continuous solutions φ : X → R of the equation φ(x) = ∫_Ω φ(f(x,ω)) P(dω).

2000 Mathematics Subject Classification.   39B12, 39B52, 60B12.

Key words and phrases.   Random-valued vector functions, sequences of iterates, iterative functional equations, continuous solutions.

DOI: 10.3336/gm.42.2.12

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