| Summary: | By using Lucas polynomials, we define a new subclass of analytic bi-univalent functions, class <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics></math></inline-formula>, 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 <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfenced close="|" open="|"><msub><mi>a</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula> and <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mfenced close="|" open="|"><msub><mi>a</mi><mn>3</mn></msub></mfenced></semantics></math></inline-formula> for the functions in this new subclass of <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="sans-serif">Σ</mi></semantics></math></inline-formula> 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.
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