Some functional inequalities and their Baire category properties
type: Item
instance of: scholarly article
title: Some functional inequalities and their Baire category properties
zbMATH Open document ID: 0860.39039
DOI: 10.1007/BF01818326
author: Bolesław Gaweł
published in: Aequationes Mathematicae
publication date: 1996-11-19T00:00:00Z
full work available at URL: https://eudml.org/doc/137654
review text: Motivated by problems related to the study of the iterative functional equation \(\varphi (f(x)) = g(x, \varphi (x))\), the author considers, from a topological point of view, the set of all continuous functions \(f:I \to I\) for which the unique continuous solution \(\psi: I\to [0,\infty]\) of the inequalities: \[ \psi \bigl(f(x) \bigr) \leq\beta \bigl(x,\psi (x)\bigr) \quad \text{and} \quad \alpha \bigl(x,\psi (x)\bigr) \leq\psi \bigl(f(x)\bigr) \leq\beta \bigl(x,\psi (x)\bigr) \] is the zero function.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 935127
zbMATH Keywords: functional inequalities
zbMATH Keywords: iterative functional equation
zbMATH Keywords: continuous solution
MaRDI profile type: Publication
cites work: The Set of all Iterates is Nowhere Dense in C([ 0, 1 ], [ 0, 1 ])
cites work: On the uniqueness of continuous solutions of functional equations
cites work: The Borel structure of iterates of continuous functions
cites work: Q5592596
cites work: Q4040882
cites work: Q3035896
cites work: Some Dual Statements Concerning Wiener Measure and Baire Category
OpenAlex ID: W2069701584
description: scientific article; zbMATH DE number 935127