Symmetrically differentiable functions with a perfect set of nondifferentiability points (Q1080543)

A function f: [a,b]\(\to R\) is said to be symmetrically differentiable at a point \(x\in [a,b]\) if there exists the finite symmetric derivative \(f_ s'(x)=\lim_{h\to 0}[f(x+h)-f(x-h)]/2h.\) The author constructs a continuous, everywhere symmetrically differentiable function \(f: R\to R\) having the properties: f is not differentiable at the points of a certain perfect set P, f is continuously differentiable in \(R\setminus P\) and f is not a function of the class \(ACG_*\) on P. The function f is also an example of an everywhere symmetrically differentiable function, whose symmetric derivative is not integrable in the Denjoy-Perron sense.