Quasiconformal extension of integral transforms of analytic and harmonic mappings

Abstract

In this article, we prove a criterion for quasiconformal extension of the integral transforms of analytic functions defined in the unit disk of the complex plane. Thereafter, we prove a sufficient condition for quasiconformal extensibility of sense-preserving harmonic mappings defined in the unit disk and applying this result, we obtain criteria for the quasiconformal extension of various types of integral transforms that are defined for sense-preserving harmonic mappings. We also study the stability of the quasiconformal extension of sense-preserving harmonic mappings.

Keywords:

• Quasiconformal extension
• harmonic mappings
• integral transforms

AMS Subject Classifications:

• 30C45
• 30C55
• 30C62
• 31A05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors would like to thank CSIR, India [Ref. No. 25(0281)/18/EMR-II] for its financial support.