DOI: 10.68381/jca28011 ISSN: 0944-6532

Asymptotic Hyers-Ulam Stability or Superstability by Unilateral Perturbations on the Concavity Side for Generalized Linear Equations

Catherine Peppo

In a recent paper [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)]} ∣ ∣ f ( x + y ) − f ( x ) − f ( y ) ∣ ∣ = B [ ϕ ( x ) + ϕ ( 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.