Lipschitzian solutions to linear iterative equations revisited

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• 作者：Karol Baron ; Janusz Morawiec
• 关键词：Iterative equations ; Lipschitzian solutions ; continuous dependence of solutions ; Bochner integral
• 刊名：Aequationes mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：91
• 期：1
• 页码：161-167
• 全文大小：443KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Combinatorics;
• 出版者：Springer International Publishing
• ISSN：1420-8903
• 卷排序：91

文摘

We study the problems of the existence, uniqueness and continuous dependence of Lipschitzian solutions \(\varphi \) of equations of the form $$\begin{aligned} \varphi (x)=\int _{\Omega }g(\omega )\varphi \big (f(x,\omega )\big )\mu (d\omega )+F(x), \end{aligned}$$where \(\mu \) is a measure on a \(\sigma \)-algebra of subsets of \(\Omega \) and \(\int _{\Omega }g(\omega )\mu (d\omega )\!=\!1\).KeywordsIterative equationsLipschitzian solutionscontinuous dependence of solutionsBochner integralMathematics Subject ClassificationPrimary 39B12Download to read the full article textReferences1.Baron, K.: On the convergence in law of iterates of random-valued functions. Aust. J. Math. Anal. Appl. 6(1), 9 (2009) (Art. 3)2.Baron, K., Morawiec, J.: Lipschitzian solutions to linear iterative equations. Publ. Math. Debr. 89(3), 277–285 (2016)MathSciNetCrossRefMATHGoogle Scholar3.Kuczma, M., Choczewski, B., Ger, R.: Iterative functional equations, Encyclopedia of Mathematics and its Applications, vol. 32. Cambridge University Press, Cambridge (1990)CrossRefMATHGoogle ScholarCopyright information© The Author(s) 2016Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.