2024/09/30 by Md Firoz Ali, Ali, Md Firoz, Md Nurezzaman +3
Mathematics · #Analytic and geometric function theory #Advanced Harmonic Analysis Research #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2409.20216
Let S^*(φ) be the class of all analytic functions f in the unit disk \mathbbD=\z∈ℂ:|z|<1\, normalized by f(0)=f'(0)-1=0 that satisfy the subordination relation zf'(z)/f(z)\precφ(z), where φ is an analytic and univalent in \mathbbD with \rm Re φ(z)>0 such that φ(\mathbbD) is symmetric with respect to the real axis and stralike with respect to 1. In the present article, we obtain the sharp estimates of the pre-Schwarzian norm of f and the Alexander transformation J[f] for functions f(z) in the class S^*(φ) when φ(z)=eλz, 0<λ≤π/2 and φ(z)=√(1+cz), 0