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Title: An application of medial limits to iterative functional equations, II
Authors: Morawiec, Janusz
Keywords: Banach limits; medial limits; iterative functional equations; bounded solutions
Issue Date: 2021
Citation: "Results in Mathematics" Vol. 76, no. 1 (2021), art. no. 47, s. 1-17
Abstract: Applying medial limits we describe bounded solutions ϕ: S → R of the functional equation ϕ(x) = Ω g(ω)ϕ(f(x, ω))dμ(ω) + G(x), where (Ω,A, μ) is a measure space, S ⊂ R, f : S × Ω → S, g: Ω → R is integrable and G: S → R is bounded. The main purpose of this paper is to extend results obtained in Morawiec (Results Math 75(3):102, 2020) to the above general functional equation in wider classes of functions and under weaker assumptions.
DOI: 10.1007/s00025-021-01354-0
ISSN: 1422-6383
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