| Summary: | In the current article, making use of certain operator, we initiate and explore a certain family <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">W</mi><mo>Σ</mo></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>h</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of holomorphic and bi-univalent functions in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">D</mi></semantics></math></inline-formula>. We establish upper bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö type inequality for functions in this family.
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