On Harmonic $\nu$-Bloch and $\nu$-Bloch-type mappings

TL;DR

This paper introduces harmonic loch-type mappings as a generalization of existing classes, explores subordination principles, and establishes Bohr's theorem for these mappings, expanding the theoretical framework in harmonic function theory.

Contribution

It generalizes harmonic loch mappings to loch-type mappings and investigates their subordination principles and Bohr's theorem, extending recent results.

Findings

Established subordination principles for harmonic loch-type mappings

Proved Bohr's theorem in a general setting for these mappings

Generalized recent results on harmonic loch-type mappings

Abstract

The aim of this paper is twofold. One is to introduce the class of harmonic $\nu$-Bloch-type mappings as a generalization of harmonic $\nu$-Bloch mappings and thereby we generalize some recent results of harmonic $1$-Bloch-type mappings investigated recently by Efraimidis et al. \cite{EGHV}. The other is to investigate some subordination principles for harmonic Bloch mappings and then establish Bohr's theorem for these mappings and in a general setting, in some cases.