Nonlinear resolvents: distortion and order of starlikeness

Abstract

This paper presents a new approach to studying nonlinear resolvents of holomorphically accretive mappings on the open unit ball of a complex Banach space. We establish a distortion theorem and apply it to address problems in geometric function theory concerning the class of resolvents. Specifically, we prove the accretivity of resolvents and provide estimates for the squeezing ratio. Further, we show that nonlinear resolvents are starlike mappings of certain order and determine lower bounds for this order.