Bi-Univalent Functions with Bounded Boundary Rotation

Abstract

We introduce a new subclass of bi-univalent functions Bᵛᵃʳᵏᵃᵖᵖᵃ,ˡᵉᶠᵗᵗʰʳᵉᵉᵗⁱᵐᵉˢᵥₐᵣᵣₕₒ,γ(η,θ,ξ) associated with bounded boundary rotation by means of a linear operator defined via the convolution with the confluent hypergeometric Mittag–Leffler function. Sharp estimates are obtained for the initial coefficients |a₂| and |a₃|, together with the Fekete–Szeg"o functional |a₃-Δ a₂²|. Several special cases are also discussed, showing that the obtained results unify and extend a number of known coefficient estimates for subclasses of bi-univalent functions.