Note on an iterative functional equation
Abstract
We study the problem of solvability of the equation
ϕ(x) = ∫Ωg(ω)ϕ(f(x,ω))P(dω) + F(x)
where P is a probability measure on a σ-algebra of subsets of Ω, assuming Hölder continuity of F on the range of f.
Keywords
iterative functional equations; Hölder continuous functions
References
K. Baron, Note on two iterative functional equations, Grazer Math. Ber. 364 (2023), 1–6.
K. Baron, J. Morawiec, Lipschitzian solutions to linear iterative equations, Publ. Math. Debrecen 89 (2016), no. 3, 277–285. DOI: 10.5486/PMD.2016.7514
K. Baron, J. Morawiec, Lipschitzian solutions to linear iterative equations revisited, Aequationes Math. 91 (2017), no. 1, 161–167. DOI: 10.1007/s00010-016-0455-6
R.M. Dudley, Real Analysis and Probability, Cambridge Studies in Advanced Mathematics 74, Cambridge University Press, Cambridge, 2002.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
https://orcid.org/0000-0002-0807-2776
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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