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

TL;DR

This paper investigates the Fekete--Szeg"{o} problem for spirallike mappings and non-linear resolvents in Banach spaces, providing inequalities and solutions for these classes of holomorphic mappings.

Contribution

It extends Fekete--Szeg"{o} inequalities to spirallike mappings relative to accretive operators and solves the problem for non-linear resolvent families in Banach spaces.

Findings

Fekete--Szeg"{o} inequalities established for spirallike mappings.

Solutions provided for Fekete--Szeg"{o} problem in non-linear resolvent families.

Results applicable to holomorphically accretive mappings 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.