Geodesic
Asymptotic Hyers-Ulam Stability or Superstability for Generalized Linear Equations by Unilateral Perturbations
Journal of convex analysis, Tome 26 (2019) no. 2, pp. 543-562
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 $$ \frac{f(x+y)} {f(x)f(y)}= [\phi(x)\phi(y)]^{B}. $$
Classification : 39B62, 26A51
Mots-clés : Hyers-Ulam stability, superstability, asymptotic stability, linear equation, exponential equation 
@article{JCA_2019_26_2_JCA_2019_26_2_a8,
     author = {C. Peppo},
     title = {Asymptotic {Hyers-Ulam} {Stability} or {Superstability} for {Generalized} {Linear} {Equations} by {Unilateral} {Perturbations}},
     journal = {Journal of convex analysis},
     pages = {543--562},
     year = {2019},
     volume = {26},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_2_JCA_2019_26_2_a8/}
}
TY  - JOUR
AU  - C. Peppo
TI  - Asymptotic Hyers-Ulam Stability or Superstability for Generalized Linear Equations by Unilateral Perturbations
JO  - Journal of convex analysis
PY  - 2019
SP  - 543
EP  - 562
VL  - 26
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JCA_2019_26_2_JCA_2019_26_2_a8/
ID  - JCA_2019_26_2_JCA_2019_26_2_a8
ER  - 
%0 Journal Article
%A C. Peppo
%T Asymptotic Hyers-Ulam Stability or Superstability for Generalized Linear Equations by Unilateral Perturbations
%J Journal of convex analysis
%D 2019
%P 543-562
%V 26
%N 2
%U http://geodesic.mathdoc.fr/item/JCA_2019_26_2_JCA_2019_26_2_a8/
%F JCA_2019_26_2_JCA_2019_26_2_a8
C. Peppo. Asymptotic Hyers-Ulam Stability or Superstability for Generalized Linear Equations by Unilateral Perturbations. Journal of convex analysis, Tome 26 (2019) no. 2, pp. 543-562. http://geodesic.mathdoc.fr/item/JCA_2019_26_2_JCA_2019_26_2_a8/