Conjecture on the starlikeness order of non-linear resolvents

Let $X$ be a complex Banach space, let ${\mathbb B}$ be its open unit ball, and let $f$ be a holomorphically accretive mapping with an isolated zero at the origin. For each $\lambda>0$, let $G_\lambda$ be the corresponding resolvent mapping.

Resolvent starlikeness conjecture. Every mapping $G_\lambda$ is starlike of order at least $\frac12$. Furthermore, the order of starlikeness of $G_\lambda$ tends to $1$ as $\lambda\to\infty$.

The conjecture proposes a multidimensional analogue of the known one-dimensional result that resolvents are starlike of order at least $\frac12$, with increasingly strong starlikeness for large resolvent parameter. Its status is not established in the supplied source.