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

We discuss on the generalized Ulam-Hyers stability for functional equations in a single variable, including the nonlinear functional equations, the linear functional equations, and a generalization of functional equation for the square root spiral. The stability results have been obtained by a fixed point method. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

We use a fixed point method, initiated in [V. Radu, Fixed Point Theory 4(2003), No.1, 91-96], to prove the generalized Ulam-Hyers stability of functional equations in single variable for mappings with values in random normed spaces. This result is then used to obtain the stability for Cauchy, quadratic and monomial functional equations. (2000): 39B52, 39B62, 39B82, 47H09. Mathematics subject classification

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