Pre-Schwarzian and Schwarzian norm Estimates for Robertson class

2025/11/19 by Ahamed, Molla Basir, Hossain, Rajesh, Wang, Xiaoyuan · 1 citation
#30C45 #30C55 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.16702

Abstract

Let A denote the class of analytic functions f on the unit disk \mathbbD=\z∈ℂ : |z|<1\, normalized by f(0)=0 and f^′(0)=1. For -π/2<α<π/2, let S_α be the subclass of A consisting of functions f that satisfy the relation Re\e^iα(1+zf^′′(z)/f^′(z))\>0 for z∈\mathbbD. In this paper, we first give an equivalent characterization for a subclass of Robertson functions; then we present the distortion and growth theorems and obtain the pre-Schwarzian and Schwarzian norms for the subclass S_α. In addition, a sharp upper bound of the Schwarzian norm for the subclass is given in terms of the value f^{′ ′}(0).

Citations

• Schwarzian Norm Estimates for Analytic Functions Associated with Convex Functions
• Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions
• Schwarzian Norm Estimate for Functions in Robertson Class
• Schwarzian derivative for convex mappings of order alpha
• Pre-Schwarzian Norm Estimates for the class of Janowski Starlike Functions
• Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm
• Sharp norm estimate of Schwarzian derivative for a class of convex functions

Cited by

• Growth, Distortion, Pre-Schwarzian and Schwarzian norm estimates for Generalized Robertson class

Related

• Schwarzian Norm Estimate for Functions in Robertson Class
• Schwarzian Norm Estimate for Functions in Generalized Robertson Class
• Schwarzian Norm Estimates for Analytic Functions Associated with Convex Functions
• Pre-Schwarzian norm estimate for certain Ma-Minda Class of functions
• Schwarzian norm estimates for some classes of analytic functions