[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b191074

SUFFICIENT CONDITIONS AND RADII PROBLEMS FOR A STARLIKE CLASS INVOLVING A DIFFERENTIAL INEQUALITY

Swaminathan, Anbhu (Department of Mathematics Indian Institute of Technology Roorkee)
Wani, Lateef Ahmad (Department of Mathematics Indian Institute of Technology Roorkee)

Publication Information

Bulletin of the Korean Mathematical Society / v.57, no.6, 2020 , pp. 1409-1426 More about this Journal

Abstract

Let 𝒜_n be the class of analytic functions f(z) of the form f(z) = z + ∑^∞_k=n+1 α_kz^k, n ∈ ℕ defined on the open unit disk 𝔻, and let $${\Omega}_n:=\{f{\in}{\mathcal{A}}_n:\|zf^{\prime}(z)-f(z)\|<{\frac{1}{2}},\;z{\in}{\mathbb{D}}\}$$. In this paper, we make use of differential subordination technique to obtain sufficient conditions for the class Ω_n. Writing Ω := Ω₁, we obtain inclusion properties of Ω with respect to functions which map 𝔻 onto certain parabolic regions and as a consequence, establish a relation connecting the parabolic starlike class 𝒮_P and the uniformly starlike UST. Various radius problems for the class Ω are considered and the sharpness of the radii estimates is obtained analytically besides graphical illustrations.

Keywords

Differential subordination; parabolic and uniform starlikenss; radius problems; cardioid;

Citations & Related Records

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