| Summary: | We introduce a new subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold">J</mi><msup><mrow><mo>Σ</mo></mrow><mrow><mi>η</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>μ</mi></mrow></msup><mrow><mo>(</mo><mover accent="true"><mi>p</mi><mo>˜</mo></mover><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of bi-univalent functions, defined by shell-like curves connected with Fibonacci numbers. Our main results in this paper include estimates of the Taylor–Maclaurin coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="|" close="|"><msub><mi>a</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="|" close="|"><msub><mi>a</mi><mn>3</mn></msub></mfenced></semantics></math></inline-formula> for functions in this subclass, as well as solutions to Fekete–Szegö functional problems. We also show novel outcomes resulting from the specialization of the parameters used in our main results.
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