Abstract
We study a new subclass of functions with symmetric points and derive an equivalent formulation of these functions in term of subordination. Moreover, we find coefficient estimates and discuss characterizations for functions belonging to this new class. We also obtain distortion and growth results. We relate our results with the existing literature of the subject.
Highlights
Introduction and DefinitionsLet H ðΔÞ represent analytic functions f in the disc Δ ≔ fz : ∣z∣
We study a new subclass of functions with symmetric points and derive an equivalent formulation of these functions in term of subordination
We have an equivalent formulation of condition (9) in terms of subordination
Summary
We find coefficient estimates and discuss characterizations for functions belonging to this new class. We denote the class of close-to-convex functions by K . Of functions defined in involving g ∈ S∗ð1/2Þ. Since g ∈ S∗ð1/2Þ, Lemma 4 proves that G ∈S∗: from (8), we see that KSPðε, ηÞ contains closeto-convex functions.
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