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Fixed points and random stability of a generalized Apollonius type quadratic functional equation. (English) Zbl 1216.39038
Summary: Using the fixed-point method, we prove the generalized Hyers-Ulam stability of a generalized Apollonius type quadratic functional equation in random Banach spaces.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46B09 Probabilistic methods in Banach space theory
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