On a parametric functional equation of Dhombres type

被引：0
作者：
P. Kahlig
J. Smítal
机构：
[1] Institute of Meteorology and Geophysics,
[2] University of Vienna,undefined
[3] UZA 2,undefined
[4] A-1090 Vienna,undefined
[5] Austria,undefined
[6] e-mail: peter.kahlig@univie.ac.at,undefined
[7] Institute of Mathematics,undefined
[8] Silesian University,undefined
[9] CZ-746 01 Opava,undefined
[10] Czech Republic,undefined
[11] e-mail: smital@fpf.slu.cz,undefined
来源：
aequationes mathematicae | 1998年 / 56卷 / 1-2期
关键词：
Functional Equation; Uniform Convergence; Real Parameter; Continuous Solution; Primary 39B22;
D O I：
10.1007/s000100050044
中图分类号：
学科分类号：
摘要：
In this paper we consider the functional equation f (x f (x)) = k f (x)2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ f : R^+ \rightarrow R^+ $$\end{document} and k > 0 is a real parameter. We give a characterization of the class of its continuous solutions, and show that there are discontinuous solutions which are strongly irregular.
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页码：63 / 68
页数：5
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