2017/03/10 by V. Ravichandran, Ravichandran, V., Shelly Verma +1
Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1703.03588
openalex publication_date 2017/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For -1 ≤ B ≤ 1 and A>B, let S^*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z) \prec (1+ A z)/(1+ B z) (|z|<1). For -1 ≤ B ≤ 11) and B=1. As an application, for F:=f-1, A= 2 β-1 (β>1) and B=1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z) \prec (1+z)/(1+B z) (|z|<1, -1 ≤ B < 1).