The Coefficients of Powers of Bazilević Functions

Mathematics

NakEun Cho¹  JiHyang Park¹  Virendra Kumar² 

[1] Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea;Department of Mathematics, Ramanujan College, University of Delhi, Kalkaji, New Delhi 110019, India;

关键词: univalent function;    starlike function;    strongly Bazilević function;    Littlewood-Paley conjecture;    Fekete-Szegö functional;   

DOI  :  10.3390/math6110263

来源: DOAJ

【 摘 要 】

In the present work, a sharp bound on the modulus of the initial coefficients for powers of strongly Bazilević functions is obtained. As an application of these results, certain conditions are investigated under which the Littlewood-Paley conjecture holds for strongly Bazilević functions for large values of the parameters involved therein. Further, sharp estimate on the generalized Fekete-Szegö functional is also derived. Relevant connections of our results with the existing ones are also made.

【 授权许可】

Unknown