On a New Subclass of m-Fold Symmetric Biunivalent Functions Equipped with Subordinate Conditions

Document Type : Original Article

Authors

Emeka Mazi ¹

Şahsene Altinkaya ²

¹ Department of Mathematics, Faculty of Science, University of Ilorin, Nigeria

² Department of Mathematics, Faculty of Science, Uludag University, 16059, Bursa, Turkey.

10.22034/kjm.2018.63470

Abstract

In this paper, we introduce a new subclass of biunivalent function class $\Sigma$ in which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric analytic functions. For functions of the subclass introduced in this paper, we obtain the coefficient bounds for $|a_{m+1}|$ and $|a_{2m+1}|$ and also study the Fekete-Szegö functional estimate for this class. Consequences of the results are also discussed.

Keywords

Biunivalent functions

coefficient bounds

pseudo-starlike functions

Fekete-Szegö functional estimates

Taylor-Maclaurin coefficients

subordination

Subjects

• 30 Functions of a complex variable

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