Stability for a family of equations generalizing the equation of p-Wright affine functions

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 *-homomorphisms of C*-algebras. The main tool in the proofs is a fixed point result in BrzdÈ©k, Chudziak, Páles (2011).