Application of Einstein Function on Bi-Univalent Functions Defined on the Unit Disc

Abstract

Motivated by q-calculus, we define a new family of Σ, which is the family of bi-univalent analytic functions in the open unit disc U that is related to the Einstein function E(z). We establish estimates for the first two Taylor–Maclaurin coefficients |a2|, |a3|, and the Fekete–Szegö inequality a3−μa22 for the functions that belong to these families.

Keywords

• analytic function
• Einstein function
• bernoulli numbers
• bi-univalent function
• quantum calculus
• subordination