Certain subclasses of bi-close-to-convex functions associated with quasi-subordination. (English) Zbl 1474.30122

Summary: In the present investigation, we introduce certain new subclasses of the class of biunivalent functions in the open unit disc \(U = \{z : |z| < 1\}\) defined by quasi-subordination. We obtained estimates on the initial coefficients \(|a_2|\) and \(|a_3|\) for the functions in these subclasses. The results present in this paper would generalize and improve those in related works of several earlier authors.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
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