Asymptotic Hyers-Ulam Stability or Superstability for Generalized Linear Equations by Unilateral Perturbations

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

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}. f ( x + y ) f ( x ) f ( y ) = [ ϕ ( x ) ϕ ( y ) ] B .