Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination

Abstract

Two quasi-subordination subclasses QΣ γ,k α,β (ϑ, ρ; φ) and MΣ γ,k α,β (τ, ϑ, ρ; φ) of the class Σ of analytic and bi-univalent functions associated with the convolution operator involving Mittag-Leffler function are introduced and investigated. Then, the corresponding bound estimates of the coefficients a 2 and a 3 are provided. Meanwhile, Fekete-Szeg ö functional inequalities for these classes are proved. Besides, some consequences and connections to all the theorems would be interpreted, which generalize and improve earlier known results.

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