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In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad family of many well-known linear positive operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta, Lupaş-Beta, Lupaş-Szász, genuine Bernstein-Durrmeyer, and Pǎltǎnea. We first find direct estimates in terms of the second-order modulus of continuity, then we find an estimate of error in the Ditzian-Totik modulus of smoothness. Then we discuss the rate of approximation for functions in the Lipschitz class. Furthermore, we study the pointwise Grüss-Voronovskaja-type result and also establish the Grüss-Voronovskaja-type asymptotic formula in quantitative form.

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<p style='text-indent:20px;'>In the present article, we study a generalization of Szász operators by Gould-Hopper polynomials. First, we obtain an estimate of error of the rate of convergence by these operators in terms of first order and second order moduli of continuity. Then, we derive a Voronovkaya-type theorem for these operators. Lastly, we derive Grüss-Voronovskaya type approximation theorem and Grüss-Voronovskaya type asymptotic result in quantitative form.</p>