An approximation property of exponential functions
type: Item
instance of: scholarly article
title: An approximation property of exponential functions
zbMATH Open document ID: 1224.41061
published in: Acta Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: Using the power series method, the author gives a solution of the linear differential equation \[ y'(x)- \lambda y(x)= \sum_{n=0}^{\infty}a_n(x-c)^n, \] where \(y\) is a function from the real interval \((c-\rho, c+\rho)\) into the set of complex numbers, where \(\rho\) is the radius of convergence of the series on the right hand side of the equation and \(\lambda\) is a complex number. Moreover, in appropriate class of analytic functions, the author investigates the stability in Hyers-Ulam's sence of the equation \(y'(x) - \lambda y(x)=0.\)
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 5652041
zbMATH Keywords: linear first order differential equation
zbMATH Keywords: power series method
zbMATH Keywords: exponential function
zbMATH Keywords: approximation
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: local Hyers-Ulam stability
author: Soon-Mo Jung
reviewed by: Józef Myjak
MaRDI profile type: Publication
full work available at URL: s10474-009-8167-1
OpenAlex ID: W1965943437
cites work: On some inequalities and stability results related to the exponential function
cites work: Stability of functional equations in several variables
cites work: Hyers-Ulam-Rassias stability of functional equations in mathematical analysis
cites work: Q5690493
cites work: HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′ = λy
cites work: Hyers stability of the linear differential equation
cites work: Connections between Hyers and Lyapunov stability of the ordinary differential equations.
cites work: Q4122117
cites work: ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy
cites work: Q4486743
DOI: 10.1007/S10474-009-8167-1
description: scientific article; zbMATH DE number 5652041