Sufficient conditions for ϵ quasi-convex mappings in a complex Banach space

Abstract

In this article, some sufficient conditions for ϵ quasi-convex mappings on the unit ball B in a complex Banach space are provided. From these, we may construct many concrete ϵ quasi-convex mappings on B. Some results, presented in this article, generalize the related results of earlier authors.

Keywords:

• locally biholomorphic mapping
• biholomorphic mapping
• starlike mapping
• quasi-convex mapping
• ϵ quasi-convex mapping

AMS Subject Classifications::

• 32A30
• 32H02
• 30C45

Acknowledgements

The authors thank the referees for their helpful comments and suggestions to improve our manuscript.