Abstract
In this paper, we derive a bound of the fourth Hankel determinant for the class of star-like functions. We also consider this problem for 2-fold and3-fold symmetric star-like functions. In this case, we obtain sharp results.
Highlights
Introduction and DefinitionsLet A denote the class of all analytic functions f of the form ∞f(z) z + anzn, (z ∈ D), (1)n 2 which are analytic in the open unit disc D {z ∈ C: |z| < 1}
Let S∗, C, and K denote the classes of star-like, convex, and close-to-convex functions, respectively, which are defined as follows: S∗
Let P denote the class of all analytic functions p of the form p(z) 1 + cnzn, z ∈ D, (3)
Summary
Let A denote the class of all analytic functions f of the form f(z) z + anzn, (z ∈ D), (1) Let S denote the subclass of all univalent functions in A. Let S∗, C, and K denote the classes of star-like, convex, and close-to-convex functions, respectively, which are defined as follows: S∗ Let P denote the class of all analytic functions p of the form p(z) 1 + cnzn, z ∈ D, (3)
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