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A fixed point approach to the stability of quadratic functional equation with involution. (English) Zbl 1149.39022

Summary: L. Cădariu and V. Radu [Grazer Math. Ber. 346, 43–52 (2004; Zbl 1060.39028)] applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation with involution.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
54E35 Metric spaces, metrizability
39B52 Functional equations for functions with more general domains and/or ranges
54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 1060.39028
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References:

[3] doi:10.2307/2042795 · Zbl 0398.47040 · doi:10.2307/2042795
[4] doi:10.1007/BF01831117 · Zbl 0836.39007 · doi:10.1007/BF01831117
[6] doi:10.1007/BF01830975 · Zbl 0806.47056 · doi:10.1007/BF01830975
[11] doi:10.1007/BF02755452 · Zbl 0899.39007 · doi:10.1007/BF02755452
[12] doi:10.1155/S0161171296000324 · Zbl 0843.47036 · doi:10.1155/S0161171296000324
[13] doi:10.1090/S0002-9904-1968-11933-0 · Zbl 0157.29904 · doi:10.1090/S0002-9904-1968-11933-0
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