Fixed points of an integral operator
type: Item
instance of: scholarly article
title: Fixed points of an integral operator
zbMATH Open document ID: 1060.45002
DOI: 10.1007/BF02788784
author: Miroljub Jevtić
published in: Journal d'Analyse Mathématique
publication date: 2004-09-27T00:00:00Z
review text: The author studies the equation \[ g(x)=(1-x)^{\gamma}\frac{\gamma}{2}\int_{0}^{1} \frac{1+tx}{(1-tx)^{\gamma+1}}g(t)t^{\gamma/2-1}\,dt, \qquad \gamma \geq 2, \] arising naturally in the study of the invariant-mean-value properties of hyperbolically-harmonic function. The main result establishes necessary and sufficient conditions (in terms of \(\gamma\)) of the following property: constants are the only \(L^{1}([0,1])\)-solutions of this equation.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 45C05
zbMATH DE Number: 2103491
zbMATH Keywords: integral equation
zbMATH Keywords: hyperbolically-harmonic function
zbMATH Keywords: eigenvalue
zbMATH Keywords: integrable solution
zbMATH Keywords: fixed points
zbMATH Keywords: integral operator
MaRDI profile type: Publication
cites work: An invariant volume-mean-value property
cites work: Q3665386
cites work: Q4023465
cites work: Commuting Toeplitz operators with harmonic symbols
cites work: Q5182498
cites work: Q5847356
cites work: Q4857214
cites work: Q3958740
cites work: Q4340096
Recommended article: Q4703578
Recommended article: Q3604115
Recommended article: Q4214518
Recommended article: Q4818776
Recommended article: Fixed points for operators in a space of continuous functions and applications
Recommended article: Fixed point theorem utilizing operators and functionals
Recommended article: Q3615592
Recommended article: Q4469037
Recommended article: Q3784699
Recommended article: Fixed-points of Set-continuous Operators
description: scientific article; zbMATH DE number 2103491