(H,G)-coincidence theorems for free G-spaces

Let us consider G a group acting freely on a Hausdorff paracompact topological space X and let Y be a k-dimensional metrizable space (or k-dimensional CW-complex). In this paper, by using the genus of X  , gen(X,G), we prove (H,G)(H,G)-coincidence theorems for maps f:X→Yf:X→Y. Such theorems generalize the main theorem proved by Aarts, Fokkink and Vermeer in [1] and the main result proved by dos Santos and Coelho in [11].