2024/02/19 by Ahamed, Molla Basir, Roy, Partha Pratim
#30C50 #30C80 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30C45
paper · doi:10.48550/arxiv.2402.11808
Let H(Ω) be the class of complex-valued functions harmonic in Ω⊂ℂ and each f=h+g∈ H(Ω), where h and g are analytic. In the study of Bohr phenomenon for certain class of harmonic mappings, it is to find a constant rf∈ (0, 1) such that the inequality Mf(r):=r+∑n=2∞(|an|+|bn|)rn≤ d(f(0), ∂Ω) for |z|=r≤ rf, where d(f(0), ∂Ω) is the Euclidean distance between f(0) and the boundary of Ω:=f(\mathbbD) . The largest such radius rf is called the Bohr radius and the inequality Mf(r)≤ d(f(0), ∂Ω) is called the Bohr inequality for the class H(Ω) . In this paper, we study Bohr phenomenon for the class of close-to-convex harmonic mappings establishing several inequalities. All the results are proved to be sharp.