Fixed point methods for the generalized stability of functional equations in a single variable. (English) Zbl 1146.39040

Summary: We discuss 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.


39B82 Stability, separation, extension, and related topics for functional equations
39B22 Functional equations for real functions
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