Linearly invariant families and harmonic Bloch mappings on hyperbolic domain

Authors

  • Bappaditya Bhowmik Department of Mathematics, Indian Institute of Technology Kharagpur, India
  • Sambhunath Sen Department of Mathematics, Indian Institute of Technology Kharagpur, India

DOI:

https://doi.org/10.3842/umzh.v77i7.8707

Keywords:

Bloch function, Harmonic Bloch mapping, Linearly invariant family

Abstract

UDC 517.5

We extend the notions of harmonic Bloch, harmonic Bloch-type mappings, and a linearly invariant family of harmonic mappings defined in the open unit disc $\mathbb D$ of the complex plane to a  hyperbolic domain of the complex plane.  Then we establish the relation between linearly invariant family of holomorphic functions with harmonic Bloch mappings and a linearly invariant family of harmonic mappings with  harmonic Bloch-type mappings  defined on a  hyperbolic domain of the complex plane. We also prove that the bounds of the Bloch seminorms for  harmonic Bloch and harmonic Bloch-type mappings depend on the order of the linearly invariant family of holomorphic functions and the order of the linearly invariant family of harmonic mappings, respectively.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 7, 2025.

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Published

27.08.2025

Issue

Vol. 77 No. 7 (2025)

Section

Research articles

License

Copyright (c) 2025 Bappaditya Bhowmik, Sambhunath Sen

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Bhowmik, Bappaditya, and Sambhunath Sen. “Linearly Invariant Families and Harmonic Bloch Mappings on Hyperbolic Domain”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 7, Aug. 2025, pp. 490–491, https://doi.org/10.3842/umzh.v77i7.8707.