2024/08/27 by Molla Basir Ahamed, Partha Pratim Roy, Ahamed, Molla Basir +1
Mathematics · #30C80 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary 30C45
paper · pdf · doi:10.48550/arxiv.2408.14773
openalex publication_date 2024/08/27 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28
The Bohr radius for an arbitrary class F of analytic functions of the form f(z)=∑n=0∞anzn on the unit disk \mathbbD=\z∈ℂ : |z|<1\ is the largest radius RF such that every function f\inF satisfies the inequality d(∑n=0∞|anzn|, |f(0)|)=∑n=1∞|anzn|≤ d(f(0), ∂ f(\mathbbD)), for all |z|=r≤ RF , where d(0, ∂ f(\mathbbD)) is the Euclidean distance. In this paper, our aim is to determine the sharp improved Bohr radius for the classes of analytic functions f satisfying differential subordination relation zf′(z)/f(z)\prec h(z) and f(z)+βzf′(z)+γz2f′′(z)\prec h(z), where h is the Janowski function. We show that improved Bohr radius can be obtained for Janowski functions as root of an equation involving Bessel function of first kind. Analogues results are obtained in this paper for α-convex functions and typically real functions, respectively. All obtained results in the paper are sharp and are improved version of [Bull. Malays. Math. Sci. Soc. (2021) 44:1771-1785].