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Fekete-Szeg¨o Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination

B. Srutha Keerthi, P. Lokesh

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Abstract

An analytic function f is quasi-subordinate to an analytic function g, in the open unit disk if there exist analytic functions I• and w, with |I•(z)| ≤ 1, w(0) = 0 and |w(z)| < 1 such that f(z) = I•(z)g(w(z)). Certain subclass of analytic univalent functions associated with quasisubordination are defined and the bounds for the Fekete-Szeg¨o coefficient functional |a3 − µa2 2 | for functions belonging to these subclass is derived.

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What this paper is about

An analytic function f is quasi-subordinate to an analytic function g, in the open unit disk if there exist analytic functions I• and w, with |I•(z)| ≤ 1, w(0) = 0 and |w(z)| < 1 such that f(z) = I•(z)g(w(z)). Certain subclass of analytic univalent functions associated with quasisubordination are defined and the bounds for the Fekete-Szeg¨o coefficient functional |a3 − µa2 2 | for functions belonging to these subclass is derived.

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Available abstract

An analytic function f is quasi-subordinate to an analytic function g, in the open unit disk if there exist analytic functions I• and w, with |I•(z)| ≤ 1, w(0) = 0 and |w(z)| < 1 such that f(z) = I•(z)g(w(z)). Certain subclass of analytic univalent functions associated with quasisubordination are defined and the bounds for the Fekete-Szeg¨o coefficient functional |a3 − µa2 2 | for functions belonging to these subclass is derived.

Key concepts: Subclass, Subordination (linguistics), Analytic function, Unit disk, Mathematics, Univalent function, Quasi-analytic function, Function (biology)

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