Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric \(q\)-derivative operator. (English) Zbl 1488.30130
Summary: In this paper, we discuss the various properties of a newly-constructed subclass of the class of normalized bi-univalent functions in the open unit disk, which is defined here by using a symmetric basic (or \(q\)-) derivative operator. Moreover, for functions belonging to this new basic (or \(q\)-) class of normalized biunivalent functions, we investigate the estimates and inequalities involving the second Hankel determinant.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 05A30 | \(q\)-calculus and related topics |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 33D15 | Basic hypergeometric functions in one variable, \({}_r\phi_s\) |
Keywords:
analytic functions; univalent functions; bi-univalent functions; Hankel determinant; Fekete-Szegö functional; \(q\)-derivativeReferences:
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