Strong pseudo-contractions perturbed by compact operators in Banach spaces

Let $X$ be a (real) Banach space, let $D$ be an open subset of $X$, and let $\mathcal{B}(X)$ denote the collection of all nonempty bounded and closed subsets of $X$. Suppose $T$ is continuous from $\overline{D}$ into $\mathcal{B}(X)$ with respect to the Hausdorff metric and strongly pseudo-contractive, while $g$ is compact from $\overline{D}$ into $X$. Then $T+g$ has a fixed point if it satisfies the classical Leray-Schauder condition on the boundary of $D$.