2018/11/03 by Rahim Kargar, Kargar, R., Janusz Sokół +3
Materials Science · Mathematics · #30C45 #30C50 #Analytic and geometric function theory #Complex Variables (math.CV) #Crystal Structures and Properties #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1811.01271
openalex publication_date 2018/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Let S^*(α1,α2), where α1, α2 ∈ (0,1], represent the class of functions f that are analytic in the open unit disk \mathbbD, normalized by f(0) = f'(0) - 1=0, and satisfying the following double-sided inequality: -(πα1)/(2)lt; arg\(zf'(z))/(f(z))\ lt;(πα2)/(2), (z∈\mathbbD). In this manuscript, we estimate the coefficients and logarithmic coefficients associated with functions that belong to the class S^*(α1,α2). As a result, we provide a general bound for the coefficients of a strongly starlike function, which has been an open question until now. Finally, we derive upper and lower bounds for the expression \rm Re\zf'(z)/f(z)\, where f∈ S^*(α1,α2).