New family of bi-univalent functions with respect to symmetric conjugate points associated with Borel distribution

Abstract

In this paper, we introduce and investigate a new family, denoted by 𝒲Σsc (λ, η, δ, r), of normalized holomorphic and bi-univalent functions with respect to symmetric conjugate points, defined in 𝕌, by making use the Borel distribution series, which is associated with the Horadam polynomials. We derive estimates on the initial Taylor-Maclaurin coefficients and solve the Fekete-Szeg˝o type inequalities for functions in this family.

Keywords

• holormorphic function
• bi-univalent function
• upper bounds
• fekete-szeg˝o functional
• symmetric conjugate points
• borel distribution
• horadam polynomials
• coefficient estimates
• 30c45
• 30c20