| Summary: | Some well-known authors have extensively used orthogonal polynomials in the framework of geometric function theory. We are motivated by the previous research that has been conducted and, in this study, we solve the Fekete–Szegö problem as well as give bound estimates for the coefficients and an upper bound estimate for the second Hankel determinant for functions in the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">G</mi><mo>Σ</mo></msub><mrow><mo>(</mo><mi>v</mi><mo>,</mo><mi>σ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of analytical and bi-univalent functions, implicating the Euler polynomials.
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