ABSTRACT
The real exponential function f(x)=exhttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003120179/2f64eb1a-b420-42b6-b5e6-8e0749ecce36/content/math2_1.tif"/> is the only nontrivial solution of the differential equation f′=fhttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003120179/2f64eb1a-b420-42b6-b5e6-8e0749ecce36/content/math2_2.tif"/> and the objective is to go through the the Hyers-Ulam stability of this equation, i.e. to solve for a given ε>0https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003120179/2f64eb1a-b420-42b6-b5e6-8e0749ecce36/content/math2_3.tif"/> the inequality |f′(x)−f(x)|≤εhttps://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003120179/2f64eb1a-b420-42b6-b5e6-8e0749ecce36/content/math2_4.tif"/>
