| Summary: | We construct the Stancu-type generalization of <i>q</i>-Bernstein operators involving the idea of Bézier bases depending on the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>1</mn><mo>≤</mo><mi>ζ</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> and obtain auxiliary lemmas. We discuss the local approximation results in term of a Lipschitz-type function based on two parameters and a Lipschitz-type maximal function, as well as other related results for our newly constructed operators. Moreover, we determine the rate of convergence of our operators by means of Peetre’s <i>K</i>-functional and corresponding modulus of continuity.
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