2022/12/12 by Ahamed, Molla Basir · 1 citation
#30C45 #30C50 #30C80 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2212.05710
A class F consisting of analytic functions f(z)=∑n=0∞anzn in the unit disc \mathbbD=\z∈ℂ:|z|<1\ satisfies a Bohr phenomenon if there exists an rf>0 such that If(r):=∑n=1∞|an|rn≤d(f(0),∂ \mathbbD) for every function f\inF , and |z|=r≤ rf . The largest radius rf is the Bohr radius and the inequality If(r)≤d(f(0),∂ \mathbbD) is Bohr inequality for the class F , where ` d ' is the Euclidean distance. If there exists a positive real number r0 such that If(r)≤ d(f(0),∂ \mathbbD) holds for every element of the class F for 0≤ rr0 , then we say that r0 is sharp bound for the inequality w.r.t. the class F . In this paper, we prove sharp refinement of the Bohr-Rogosinski inequality for certain classes of harmonic mappings.