2025/06/23 by Ahamed, Molla Basir, Hossain, Rajesh, Ahammed, Sabir · 2 citations
#30C55 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30C45
paper · doi:10.48550/arxiv.2506.19873
Let A denote the class of analytic functions f on the unit disc \mathbbD=\z∈ℂ: |z|<1\ normalized by f(0)=0 and f′(0)=1. In the present article, we consider and F(c) the subclasses of A are defined by F(c)=\f\inA: \rm Re (1+\fraczf′′(z)f′(z))gt;1-(c)/(2), for some c∈(0,3]\, and derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives for functions in and F(c) expressed in terms of their value f′′(0), in particular, when the quantity is equal to zero. Moreover, we obtain sharp bounds for distortion and growth theorems for functions in the class F(c).