On the stability of the additive Cauchy functional equation in random normed spaces. (English) Zbl 1139.39040

Miheţ, Dorel; Radu, Viorel

J. Math. Anal. Appl. 343, No. 1, 567-572 (2008).

Summary: Some stability results for the functional equations of Cauchy and Jensen in probabilistic setting are proved by using the fixed point method.

MSC:

39B82	Stability, separation, extension, and related topics for functional equations
39B52	Functional equations for functions with more general domains and/or ranges
60H25	Random operators and equations (aspects of stochastic analysis)

Keywords:

generalized stability; random normed space; probabilistic Cauchy functional equation; probabilistic Jensen functional equation; fixed point method

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