  Functions satisfying a defective renewal equation arise commonly in applied
probability models. Usually these functions don't admit a explicit expression.
In this work we consider to approximate them by means of a gamma-type operator
given in terms of the Laplace transform of the initial function. We investigate
which conditions on the initial parameters of the renewal equation give optimal
order of uniform convergence in the approximation. We apply our results to ruin
probability in the classical risk model, paying special attention to mixtures
of gamma claim amounts.
