We prove, using the fixed point approach, some stability results for the general linear functional equation. Namely we obtain sufficient conditions for the stability of a wide class of functional equations and control functions. Our results generalize a lot of the well known and recent outcomes concerning stability. In some examples we indicate how our method may be used to check if the particular functional equation is stable and we discuss the optimality of obtained bounding constants.
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Bahyrycz et al. (2014) studied this question.
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