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Title: An Application of Medial Limits to Iterative Functional Equations
Authors: Morawiec, Janusz
Keywords: Banach limits; medial limits; iterative functional equations; bounded solutions
Issue Date: 2020
Citation: Results in Mathematics, Vol. 75 (2020), Art. No. 102
Abstract: Assume that (Ω,A, P) is a probability space, f : [0, 1] × Ω → [0, 1] is a function such that f(0, ω) = 0, f(1, ω) = 1 for every ω ∈ Ω, g: [0, 1] → R is a bounded function such that g(0) = g(1) = 0, and a, b ∈ R. Applying medial limits we describe bounded solutions ϕ: [0, 1] → R of the equation ϕ(x) = Ω ϕ(f(x, ω))dP(ω) + g(x) satisfying the boundary conditions ϕ(0) = a and ϕ(1) = b.
DOI: 10.1007/s00025-020-01229-w
ISSN: 1422-6383
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