Abstract
We study the problems of the existence, uniqueness and continuous dependence of Lipschitzian solutions \(\varphi \) of equations of the form
where \(\mu \) is a measure on a \(\sigma \)-algebra of subsets of \(\Omega \) and \(\int _{\Omega }g(\omega )\mu (d\omega )\!=\!1\).
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Baron, K., Morawiec, J.: Lipschitzian solutions to linear iterative equations. Publ. Math. Debr. 89(3), 277–285 (2016)
Kuczma, M., Choczewski, B., Ger, R.: Iterative functional equations, Encyclopedia of Mathematics and its Applications, vol. 32. Cambridge University Press, Cambridge (1990)
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Baron, K., Morawiec, J. Lipschitzian solutions to linear iterative equations revisited. Aequat. Math. 91, 161–167 (2017). https://doi.org/10.1007/s00010-016-0455-6
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DOI: https://doi.org/10.1007/s00010-016-0455-6