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The main goal of this investigation is to obtain sharp upper bounds for Fekete-Szegö functional and the third Hankel determinant for a certain subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">SL</mi><mo>∗</mo></msup><mfenced separators="" open="(" close=")"><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>α</mi></mfenced></mrow></semantics></math></inline-formula> of holomorphic functions defined by the Carlson-Shaffer operator in the unit disk. Finally, for some special values of parameters, several corollaries were presented.