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Stability of functional equations in dislocated quasi-metric spaces. (English) Zbl 06946314
Summary: We present a result on the generalized Hyers-Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove stability of the Cauchy functional equation and the linear functional equation in two variables, also for functions taking values in a complete dislocated quasimetric space. In this way we generalize some earlier results proved for classical complete metric spaces.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
54E50 Complete metric spaces
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