| Summary: | In this paper, we give some correct quantum type Simpson’s inequalities via the application of <i>q</i>-Hölder’s inequality. The inequalities of this study are compatible with famous Simpson’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>8</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>/</mo><mn>8</mn></mrow></semantics></math></inline-formula> quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of Hölder’s inequality in the quantum framework.
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