
Journal of Convex Analysis 26 (2019), No. 2, 543562 Copyright Heldermann Verlag 2019 Asymptotic HyersUlam Stability or Superstability for Generalized Linear Equations by Unilateral Perturbations Cathérine Peppo Itescia, 8 rue P. de Coubertin, 95300 Pontoise, France cpeppo@cciparisidf.fr [Abstractpdf] In relation to the famous problem of Ulam ``Give conditions in order for a linear mapping near an approximated linear mapping to exist'', we consider the stability or superstability of generalized linear equation \begin{center} $f(x+y)f(x)f(y)=B[\phi(x)+\phi(y)]$ \end{center} by left or right perturbations with some hypotheses of convexity or concavity, and  in a forthcoming paper  apply our conclusions to the generalized exponential equation $$ \frac{f(x+y)} {f(x)f(y)}= [\phi(x)\phi(y)]^{B}. $$ Keywords: HyersUlam stability, superstability, asymptotic stability, linear equation, exponential equation. MSC: 39B62, 26A51 [ Fulltextpdf (132 KB)] for subscribers only. 