• On the coefficient conjecture of Clunie and Sheil-Small on univalent harmonic mappings

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      https://www.ias.ac.in/article/fulltext/pmsc/125/03/0277-0290

    • Keywords

       

      Harmonic functions; stable harmonic functions; harmonic univalent; harmonic convex; convex in one direction; growth and covering theorems; coefficient bound.

    • Abstract

       

      In this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for a class of univalent harmonic functions which includes functions convex in some direction. Next, we prove growth and covering theorems and some related results. Finally, we propose two conjectures, an affirmative answer to one of which would then imply, for example, a solution to the conjecture of Clunie and Sheil-Small.

    • Author Affiliations

       

      S Ponnusamy1 A Sairam Kaliraj2

      1. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India
      2. Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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