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Ma-Minda starlikeness of certain analytic functions

Baskar Babujee Janani, V. Ravichandran · 2025 📄 DOI →

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Ma-Minda φ-classes studied in this paper:
Exponential starlike — φ(z) = e^z ✓
Abstract

A normalized analytic function defined on the open unit disc D is called Ma-Minda starlike if zf ′(z)/f(z) is subordinate to the function ϕ. For a normalized convex function f defined on D and α > 0, we determine the radius of Ma-Minda starlikeness of the function g defined as g(z) = (zf ′(z)/f(z))α f(z) for certain choices of ϕ. In particular, we investigate the radius of Janowski starlikeness of the function g. Mathematics Subject Classification (2010): 30C80, 30C45.

Results & Lemmas (3)

Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.

Lemma 1.1. Lemma 1.1. [16] If p ∈P[A, B], then p(z) −1 −ABr2 1 −B2r2 ⩽(A −B)r 1 −B2r2 (|z| ⩽r < 1). The class of functions f ∈A with the property that…
Lemma 1.1. [16] If p ∈P[A, B], then p(z) −1 −ABr2 1 −B2r2 ⩽(A −B)r 1 −B2r2 (|z| ⩽r < 1). The class of functions f ∈A with the property that zf ′(z)/f(z)/ ∈P[A, B] is denoted by ST [A, B]. In this manuscript, we are interested in the class J α 1 defined as follows: J α 1 :=  g ∈A : g(z) = zf ′(z)
Theorem 2.1. Theorem 2.1. The ST [A, B] radius of the class J α 1, α > 0, is given by RST [A,B] = A −B 1 + α + |A + αB|.
Theorem 2.1. The ST [A, B] radius of the class J α 1 , α > 0, is given by RST [A,B] = A −B 1 + α + |A + αB|.
Theorem 2.2. Theorem 2.2. Let α > 0. For the class J α 1, the following radius results hold: 1. The ST e radius is given by RST e = ( e−1 eα+1 if α ⩾1…
Theorem 2.2. Let α > 0. For the class J α 1 , the following radius results hold: 1. The ST e radius is given by RST e = ( e−1 eα+1 if α ⩾1 e−1 e+α if α ⩽1.

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