Loewner chain and quasiconformal extension of some classes of univalent functions

ABSTRACT

In this article, we obtain quasiconformal extensions of some classes of conformal maps defined either on the unit disc or on the exterior of it onto the extended complex plane. Some of these extensions have been obtained by constructing suitable Loewner chains and others have been found by applying a well-known result.

COMMUNICATED BY:

• V. Bolotnikov

KEYWORDS:

• Loewner Chain
• meromorphic
• quasiconformal

AMS SUBJECT CLASSIFICATIONS:

• 30C62
• 30C55

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author of this article would like to thank Council for Scientific and Industrial Research (CSIR), India (Ref.No.-25(0281)/18/EMR-II) for its financial support.