Applications of Laguerre Polynomials for Bazilevič and <i>θ</i>-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi-Type Functions

Abstract

The aim of the present article is to introduce and investigate a new family LΣ(δ,η,θ,t;h) of normalized holomorphic and bi-univalent functions that involve the Sakaguchi-type Bazilevič functions and Sakaguchi-type θ-pseudo-starlike functions associated with Laguerre polynomials. We obtain estimates on the initial Taylor–Maclaurin coefficients and the Fekete–Szegö problem for functions in this family. Properties of symmetry can be studied for this newly family of functions.

Keywords

• bi-univalent function
• Fekete–Szegö problem
• Bazilevič functions
• holomorphic, regular, analytic
• <i>θ</i>-pseudo-starlike functions
• Laguerre polynomial