The general solution of the generalized Schilling's equation
type: Item
instance of: scholarly article
title: The general solution of the generalized Schilling's equation
zbMATH Open document ID: 0765.39004
DOI: 10.1007/BF01830988
author: Andrzej Grząślewicz
published in: Aequationes Mathematicae
publication date: 1993-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137501
review text: The author extends a result which he presented at the 1991 Koninki (Poland) International Conference on Functional Equations and Inequalities (ICFEI). As generalization of ``Schilling's functional equation'', which arose from Physics, he offers the general solution of the equation \(Af(qx)=B(f(x+1)+Cf(x-1)+Df(x)\) \((x\in\mathbb{R})\), where \(A,D\in\mathbb{R}\), \(B,C\in\mathbb{R}\backslash\{0\}\), \(q\in[0,1]\) are otherwise arbitrary constants, and notes that it is determined by its values on [0,1].
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 149480
zbMATH Keywords: functional equation in a single variable
zbMATH Keywords: restriction
zbMATH Keywords: induction
zbMATH Keywords: equivalent conditions
zbMATH Keywords: Schilling's functional equation
MaRDI profile type: Publication
OpenAlex ID: W2124885178
description: scientific article; zbMATH DE number 149480