The Fekete-Szego problem for spirallike mappings and non-linear resolvents in Banach spaces

Abstract

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.