On the evaluation of Tornheim sums and allied double sums

The object of study in this paper is some Tornheim type sums (sum_{n=1}^{infty}sum_{m=1}^{infty} frac{1}{n^{r}m^{s}(n+m)^{t}}) which are close relatives of the so-called Euler sums (sum_{n=1}^{infty}frac{1}{n^{s}}sum_{m=1}^{infty}frac{1}{m^{t}}). Closed form evaluations of several such double sums are obtained using elementary summation techniques earlier developed by the same author.