Geodesic
Asymptotic Hyers-Ulam Stability or Superstability by Unilateral Perturbations on the Concavity Side for Generalized Linear Equations
Journal of convex analysis, Tome 28 (2021) no. 1, pp. 143-156
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In a recent paper [{\it Asymptotic Hyers-Ulam stability or superstability for generalized linear equations by unilateral perturbations}, J. Convex Analysis 26 (2019) 543--562] we considered in relation to the famous problem of Ulam ``Give conditions in order for a linear mapping near an approximated linear mapping to exist" the stability or superstability of a generalized linear equation $$ {||{f(x+y)-f(x)-f(y)}||=B[\phi(x)+\phi(y)]} $$ by perturbations on the convexity side, named right perturbations. In this paper we continue this research for perturbations on the concavity side with some hypotheses of concavity.
Classification : 39B62, 26A51
Mots-clés : Hyers-Ulam stability, superstability, asymptotic stability, linear equation, affine equation, exponential equation 
@article{JCA_2021_28_1_JCA_2021_28_1_a10,
     author = {C. Peppo},
     title = {Asymptotic {Hyers-Ulam} {Stability} or {Superstability} by {Unilateral} {Perturbations} on the {Concavity} {Side} for {Generalized} {Linear} {Equations}},
     journal = {Journal of convex analysis},
     pages = {143--156},
     year = {2021},
     volume = {28},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a10/}
}
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C. Peppo. Asymptotic Hyers-Ulam Stability or Superstability by Unilateral Perturbations on the Concavity Side for Generalized Linear Equations. Journal of convex analysis, Tome 28 (2021) no. 1, pp. 143-156. http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a10/