caa a22 4500 606244514 CHVBK 20210128101330.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s12044-015-0236-5 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0236-5 On the coefficient conjecture of Clunie and Sheil-Small on univalent harmonic mappings [Elektronische Daten] [S PONNUSAMY, A KALIRAJ] 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. Indian Academy of Sciences, 2015 Harmonic functions nationallicence stable harmonic functions nationallicence harmonic univalent nationallicence harmonic convex nationallicence convex in one direction nationallicence growth and covering theorems nationallicence coefficient bound nationallicence PONNUSAMY S. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, 600 113, Taramani, Chennai, India aut KALIRAJ A. Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India aut Proceedings - Mathematical Sciences Springer India 125/3(2015-08-01), 277-290 0253-4142 125:3<277 2015 125 12044 https://doi.org/10.1007/s12044-015-0236-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0236-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- PONNUSAMY S. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, 600 113, Taramani, Chennai, India aut NATIONALLICENCE 700 1- KALIRAJ A. Department of Mathematics, Indian Institute of Technology Madras, 600 036, Chennai, India aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/3(2015-08-01), 277-290 0253-4142 125:3<277 2015 125 12044