Representations for the Bloch type semi-norm of Frechet differentiable mappings

TL;DR

This paper investigates the properties of Frechet differentiable mappings between normed spaces, focusing on their Bloch semi-norms and extending existing results through generalizations inspired by Pavlovic and Jocic.

Contribution

It provides new results on the Bloch semi-norm of Frechet differentiable mappings, generalizing Pavlovic's equality and Jocic's recent extensions.

Findings

Extended Pavlovic's equality to broader classes of mappings

Derived new bounds for the Bloch semi-norm in normed spaces

Connected growth control of mappings with Bloch semi-norm properties

Abstract

In this paper we give some results concerning Frechet differentiable mappings between domains in normed spaces with controlled growth. The results are mainly motivated by Pavlovic's equality for the Bloch semi-norm of continuously differentiable mappings in the Bloch class on the unit ball of the Euclidean space as well as the very recent Jocic's generalization of this result.