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Addendum to ‘On the stability of functional equations on square-symmetric groupoid’. (English) Zbl 1112.39022
Summary: Let \((X,\diamond)\) be a square-symmetric groupoid, and \((Y,*,d)\) a complete metric divisible square-symmetric groupoid. In this paper, we investigate the Hyers-Ulam stability problem, using the functional inequality \(d(g(x\diamond y),g(x)*g(y))\leq\epsilon(x,y)\) for approximate mapping \(g\colon X\to Y\) of the functional equation \(f(x\diamond y)=f(x)*f(y)\). In particular, we investigate the case of \(f(x)*f(y)=H(f(x)^{1/t},f(y)^{1/t})\) on some set \(Y\) in which \(H\:Y\times Y\to Y\) is a continuous homogeneous function of degree \(t\).

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
39B72 Systems of functional equations and inequalities
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