2020/08/01 by Allu, Vasudevarao, Halder, Himadri · 2 citations
#30C45 #30C50 #30C80 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.00187
We say that a class B of analytic functions f of the form f(z)=∑n=0∞ anzn in the unit disk \mathbbD:=\z∈ ℂ: |z|<1\ satisfies a Bohr phenomenon if for the largest radius Rf<1, the following inequality ∑n=1∞ |anzn| ≤ d(f(0),∂ f(\mathbbD) ) holds for |z|=r≤ Rf and for all functions f ∈ B. The largest radius Rf is called Bohr radius for the class B. In this article, we obtain Bohr radius for certain subclasses of close-to-convex analytic functions. We establish the Bohr phenomenon for certain analytic classes Sc*(ϕ), Cc(ϕ), Cs*(ϕ), Ks(ϕ). Using Bohr phenomenon for subordination classes \cite[Lemma 1]bhowmik-2018, we obtain some radius Rf such that Bohr phenomenon for these classes holds for |z|=r≤ Rf. Generally, in this case Rf need not be sharp, but we show that under some additional conditions on ϕ, the radius Rf becomes sharp bound. As a consequence of these results, we obtain several interesting corollaries on Bohr phenomenon for the aforesaid classes.