Preserving properties and pre-Schwarzian norms of nonlinear integral transforms

Abstract

We study preserving properties of certain nonlinear integral transforms in some classical families of normalized analytic univalent functions defined in the unit disk. Also, we find sharp pre-Schwarzian norm estimates of such integrals.

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Acknowledgement

The authors thank Professor Toshiyuki Sugawa for his useful remarks leading to some improvement in the paper.

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Correspondence to S. K. Sahoo.

Additional information

The work of the first author is supported by CSIR, New Delhi (Grant No. 09/1022(0034)/2017-EMR-I).

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Kumar, S., Sahoo, S.K. Preserving properties and pre-Schwarzian norms of nonlinear integral transforms. Acta Math. Hungar. 162, 84–97 (2020). https://doi.org/10.1007/s10474-020-01027-4

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Key words and phrases

  • integral transform
  • Hornich operator
  • Cesàro transform
  • pre-Schwarzian norm
  • univalent function
  • spirallike function
  • convex function
  • close-to-convex function

Mathematics Subject Classification

  • primary 30C55
  • 35A22
  • secondary 30C45
  • 35A23
  • 65R10