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

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.