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Dirichlet Problem, Univalency and Schwarz Lemma for Biharmonic Mappings

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Abstract

In this paper, we shall discuss the family of biharmonic mappings for which the maximum principle holds. As a consequence of our study, we present Schwarz Lemma for certain class of biharmonic mappings. Also we discuss the univalency of certain class of biharmonic mappings.

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Acknowledgements

The work of the third author is supported by Mathematical Research Impact Centric Support of DST, India (MTR/2017/000367).

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Authors and Affiliations

  1. Department of Mathematics, American University of Sharjah, 26666, Sharjah, United Arab Emirates

    Zayid Abdulhadi & Yusuf Abu Muhanna

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    Saminathan Ponnusamy

Authors
  1. Zayid Abdulhadi
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  2. Yusuf Abu Muhanna
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  3. Saminathan Ponnusamy
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Correspondence to Saminathan Ponnusamy.

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Abdulhadi, Z., Muhanna, Y.A. & Ponnusamy, S. Dirichlet Problem, Univalency and Schwarz Lemma for Biharmonic Mappings. Mediterr. J. Math. 15, 187 (2018). https://doi.org/10.1007/s00009-018-1231-8

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  • DOI: https://doi.org/10.1007/s00009-018-1231-8

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