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

Abstract

Abstract In this paper, we introduce and investigate a new family, denoted by 𝒲Σ sc (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.