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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