Addendum to ‘On the stability of functional equations on square-symmetric groupoid’

Let (X,⋄)(X,⋄) be a square-symmetric groupoid, and (Y,*,d)(Y,*,d) a complete metric divisible square-symmetric groupoid. In this paper, we obtain the Hyers–Ulam stability problem of functional inequality d(g(x⋄y),g(x)*g(y))⩽ε(x,y)d(g(x⋄y),g(x)*g(y))⩽ε(x,y) for approximate mapping View the MathML sourceg:X→Y of functional equation f(x⋄y)=f(x)*f(y)f(x⋄y)=f(x)*f(y) differing by View the MathML sourceε:X2→[0,∞). In particular, we have investigated the case of f(x)*f(y)=H(f(x)1/t,f(y)1/t)f(x)*f(y)=H(f(x)1/t,f(y)1/t) on some set YY.