Estimates on some functionals over non-linear resolvents

TL;DR

This paper provides sharp estimates for linear and quadratic functionals over non-linear resolvent classes of univalent functions, advancing understanding in geometric function theory and dynamic systems.

Contribution

It introduces new estimates for functionals over non-linear resolvent classes, a novel application in geometric function theory and dynamic systems.

Findings

Sharp estimates on early Taylor coefficients

Precise bounds on the Fekete--Szeg"o functional

Application to classes of non-linear resolvents

Abstract

Estimation of linear and quadratic functionals over different classes of univalent functions is one of the classical problems in geometric function theory. In this paper we solve the problem over some classes of so-called non-linear resolvents, which arise as a fruitful tool in dynamic systems. Sharp estimates on early Taylor coefficients and the Fekete--Szeg\"{o} functional are established.