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We present some useful techniques to revise and extend the main result on Hyers–Ulam stability of homomorphisms in p-Banach algebras [9] to quasi-Banach algebras. The techniques may be used to revise and extend other results on the stability of homomorphisms in p-Banach algebras in the literature to quasi-Banach algebras.

Let $$\mathbb {K}$$ K , $$\mathbb {F}$$ F be two fields of real or complex numbers and Xbe a normed space over field $$\mathbb {F}$$ F . In this paper, we consider the following generalized logarithmic functional equation: $$\begin{aligned} f(x^a y^b)= Af(x) + Bf(y), \end{aligned}$$ f(xayb)=Af(x)+Bf(y), where fmaps from $$\mathbb {K}$$ K into X, $$a,b\in \mathbb {Z}{\setminus }\{0\}$$ a,b∈Z\{0} and $$A, B\in \mathbb {F}$$ A,B∈F . By using the fixed point method, the generalized Hyers–Ulam stability results for such functional equation are proved.