On the difference $f(B)-f(A)$ for unbounded self-adjoint operators in the perturbation theory

The main result of the paper is the estimate
$$ \|f(B)-f(A)\|\le c\biggl[\log\biggl(1+\frac1{\|B-A\|}\biggr)+7\biggr]^2\|B-A\|, $$
obtained for Lipschitz functions, with some conditions of the growth of the functions at infinity.