An analytic functionfis quasi-subordinate to an analytic functiong, in the open unit disk if there exist analytic functionsφandw, with|φ(z)|≤1,w(0)=0and|w(z)|<1such thatf(z)=φ(z)g(w(z)). Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szegö coefficient functional|a3-μa22|for functions belonging to these subclasses are derived.

A gangadharan

Bs keerthi

S chinthamani

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Fekete-Szegö problems for quasi-subordination classes

Abstract and Applied Analysis

Let (p, q) ∈ (0, 1). Let the function f be analytic in |z| < 1. Further, let the (p, q) be differential operator defined as ∂p,qf(z)=f(pz)−f(qz)z(p−q),|z|<1. In the current investigation, the authors apply the (p, q)-differential operator for few subclasses of univalent functions defined by quasi-subordination. Initial coefficient bounds for the defined new classes are obtained. © 2018, Springer Nature Switzerland AG.

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Journal	Abstract and Applied Analysis
Publisher	Hindawi Limited
ISSN	1085-3375
Open Access	Yes