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Generalized Hyers-Ulam-Rassias theorem in Menger probabilistic normed spaces. (English) Zbl 1189.39029

Summary: We introduce two reasonable versions of approximately additive functions in a Šerstnev probabilistic normed space endowed with \(\Pi _{M}\) triangle function. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in above mentioned spaces.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
39B55 Orthogonal additivity and other conditional functional equations
46S50 Functional analysis in probabilistic metric linear spaces
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References:

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