On the stability of the mixed type functional equation in random normed spaces via fixed point method (Q2917726)

The authors investigate the stability of the functional equations NEWLINE\[NEWLINEf(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)-\varepsilon f(0)=0NEWLINE\]NEWLINE in random normed spaces, where \(\varepsilon\in\{0,1\}\) is fixed. They call solutions quadratic-additive for \(\varepsilon=0\) and general quadratic when \(\varepsilon=1\) since functions of the form \(a x^2+b x\) and \(a x^2+b x+c\) solve these equations, respectively. It seems that the authors are only interested in stability questions. In spite of the fact that the general solution of the equations could be obtained quite easily they do not solve the equations themselves. (The title is misleading: ``\dots a mixed type \dots'' would be more appropriate.)