The Davison convolution of arithmetical functions f and g is defined by \[ (f\circ g)(n)=\sum_{d| n}f(n)g(n/d)K(n,d), \] where K is a complex-valued function on the set of all ordered paris (n,d) such that n is a positive integer and d is a positive divisor of n. In this paper the arithmetical equations \(f^{(r)}=g\), \(f^{(r)}=fg\), \(f\circ g=h\) in f and the congruence (f\(\circ g)(n)\equiv 0 (mod n)\), where \(f^{(r)}\) is the iterate of f with respect to the Davison convolution, have been studied.