Coefficient Estimates for the Functions with Respect to Symmetric Conjugate Points Connected with the Combination Binomial Series and Babalola Operator and Lucas Polynomials

Abstract

By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class Σ, in the open unit disc with respect to symmetric conjugate points connected with the combination Binomial series and Babalola operator. The bounds on the initial coefficients a2 and a3 for the functions in this new subclass of Σ are investigated. Moreover, we obtain an estimation for the Fekete–Szego problem for the function subclass defined in this paper. Relevant connections of these results are presented here as corollaries.

Keywords

• symmetric conjugate points
• bi-univalent functions
• Lucas polynomials
• binomial series
• Babalola operator