Regularity properties of functional equations and inequalities
type: Item
instance of: scholarly article
title: Regularity properties of functional equations and inequalities
zbMATH Open document ID: 0676.39007
DOI: 10.1007/BF01836446
author: Karl-Goswin Grosse-Erdmann
published in: Aequationes Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137302
review text: Using \textit{R. Trautner}'s theorem [Q. J. Math. Oxf. Ser. II 38, 127-130 (1987; Zbl 0611.26002)] the author proves the main theorems: 1. Let R and T topological spaces. Suppose that R has a countable base and that X is metrizable. If g: \(X\to R\) and H: \(R\times X\to T\) are mappings were g is measurable on a set M of finite positive Haar measure and H is continuous in its first variable, then any solution f: \(X\to T\) of \(f(x\cdot y)=H(g(x),y)\) for \(x,y\in X\), is continuous. 2. Let G: \(X\times X\to R\) be a mapping. If there is a subset M of X of positive finite Haar measure, such that for each \(y\in X\) the mapping \(x\mapsto G(x,y)\) is bounded above on M, then any solution f: \(X\to R\) of f(x\(\cdot y)\leq G(x,y)\) for \(x,y\in X\), is locally bounded above.
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B72
zbMATH DE Number: 4107333
zbMATH Keywords: functional inequalities
zbMATH Keywords: continuous solution
zbMATH Keywords: locally bounded solution
zbMATH Keywords: topological spaces
zbMATH Keywords: finite positive Haar measure
MaRDI profile type: Publication
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OpenAlex ID: W2083449778
description: scientific article; zbMATH DE number 4107333