Stability for a family of equations generalizing the equation of \(p\)-Wright affine functions. (English) Zbl 1410.39044
Summary: We prove some general stability results for a family of equations, which generalizes the equation of \(p\)-Wright affine functions. In this way, we obtain some hyperstability properties for those equations, as well. We also provide some applications of those outcomes in proving inequalities characterizing the inner product spaces and stability of \(\ast\)-homomorphisms of \(C^\ast\)-algebras. The main tool in the proofs is a fixed point result in [the first author et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6728–6732 (2011; Zbl 1236.39022)].
MSC:
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
| 39B72 | Systems of functional equations and inequalities |
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 47H10 | Fixed-point theorems |
Keywords:
generalized Hyers-Ulam stability; \(p\)-Wright affine function; hyperstability; fixed pointsCitations:
Zbl 1236.39022References:
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