Criteria of Biholomorphic Convex Mappings on the bounded convex balanced domain $D_{p}^n$

TL;DR

This paper establishes new sufficient conditions for biholomorphic convex mappings on bounded convex balanced domains in complex n-space, extending previous results and providing concrete examples.

Contribution

It introduces generalized criteria for biholomorphic convex mappings on $D_{p}^n$, broadening the scope of earlier findings and including explicit examples.

Findings

New sufficient conditions for biholomorphic convex mappings

Extension of previous results in complex analysis

Concrete examples illustrating the criteria

Abstract

In this paper, we first establish several general sufficient conditions for the biholomorphic convex mappings on the bounded convex balanced domain $D_{p}^n(p_{j}\geq 2,j=1,\cdots,n)$ in $C^{n}$, which extend some related results of earlier authors. From these, some concrete examples of biholomorphic convex mappings on $D_{p}^n$ are also provided.