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A uniqueness-type problem for linear iterative equations
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Rafal Kapica
Published/Copyright:
September 25, 2009
Abstract
Given a probability space (Ω,A,P), a Polish space X and a (B(X) ⊗ A)-measurable function f:X × Ω→X we consider Borel and bounded solutions ψ:X→ℝ of the functional inequality
ψ(x) ≤ ∫Ωψ(f(x,ω))P(dω)
and a uniqueness-type problem for Borel and bounded solutions φ:X→ℝ of the functional equation
φ(x) = ∫Ωφ(f(x,ω))P(dω).
Keywords: random-valued vector functions; iterative functional equations and inequalities; bounded Borel and continuous solutions; uniqueness-type problem
Published Online: 2009-09-25
Published in Print: 2009-04
© by Oldenbourg Wissenschaftsverlag, München, Germany
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Articles in the same Issue
- Restrictions of power series and functions to algebraic surfaces
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- A Tauberian theorem for absolute quasi-Nörlund means
- Boundary Nevanlinna–Pick interpolation for Nevanlinna matrix functions and the related Hamburger matrix moment problem
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- A uniqueness-type problem for linear iterative equations
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