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

In a recent paper [Asymptotic Hyers-Ulam stability or superstability for generalized linear equations by unilateral perturbations, J. Convex Analysis 26(2) (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 parallel to f(x + y) - f(x) - f(y)parallel to = 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.