The Fekete--Szeg\"{o} problem for spirallike mappings and non-linear resolvents in Banach spaces

We study the Fekete–Szeg"{o} problem on the open unit ball of a complex Banach space. Namely, the Fekete–Szeg"{o} inequalities are proved for the class of spirallike mappings relative to an arbitrary strongly accretive operator, and some of its subclasses. Next, we consider families of non-linear resolvents for holomorphically accretive mappings vanishing at the origin. We solve the Fekete–Szeg"{o} problem over these families.