Problems similar to the additive divisor problem

For multiplicative functions ?(n), let the following conditions be satisfied: ?(n)≥0 ?(p ^r)≤A ^r,A>0, and for anyε>0 there exist constants $A_varepsilon$ ,α>0 such that $f(n) leqslant A_varepsilon n^varepsilon$ and Σ _p≤x ?(p) lnp≥αx. For such functions, the following relation is proved: $$sumlimits_{n leqslant x} {f(n)} tau (n - 1) = C(f)sumlimits_{n leqslant x} {f(n)lnx(1 + 0(1))}$$ . Hereτ(n) is the number of divisors ofn andC(?) is a constant.