Special solutions of a general iterative functional equation
type: Item
instance of: scholarly article
title: Special solutions of a general iterative functional equation
zbMATH Open document ID: 1113.39028
author: V. Murugan
author: Papagudi Venkatachalam Subrahmanyam
published in: Aequationes Mathematicae
publication date: 2007-02-14T00:00:00Z
review text: It is well known that functions satisfying formally functional equations need be neither continuous nor anywhere differentiable (in the Leibniz-Newton sense). It is, however, possible that, subject to sufficiently severe restrictions, particular solutions of functional equations may be locally similar to those of ordinary differential equations (ODEs). The existence and uniqueness theorems of this paper are established in such a framework, the key role being played by Banach's contraction principle. No concrete solution is constructed. In the introduction it is mentioned that functional equations are significant for the understanding of ``dynamical systems''. No justification is provided how time-derivatives (velocities, accelerations, induced fields, etc.) are taken into account, and how physical time enters into the considered functional equations. A reduction method is proposed for two particular functional series equations to the considered `general' form, but neither is solved. The references are limited to papers `advocating' a single ``school of thought''.
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 5126573
zbMATH Keywords: iterative functional series equation
zbMATH Keywords: differentiable solution
zbMATH Keywords: Arzela-Ascoli theorem
zbMATH Keywords: Schauder's fixed point theorem
zbMATH Keywords: Banach's Contraction Principle
reviewed by: Igor Gumowski
MaRDI profile type: Publication
full work available at URL: s00010-006-2839-5
OpenAlex ID: W2075457649
DOI: 10.1007/S00010-006-2839-5
description: scientific article; zbMATH DE number 5126573