This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas‐Buck‐type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould‐Hopper polynomials are given. Moreover, a Voronovskaya‐type result is obtained for the operators containing Gould‐Hopper polynomials.

In this work, the problem of the approximation by certain polynomials is addressed. A new type operators sequence including generalized Appell polynomials are defined, qualitative and quantitative approximation theorems are proved. Some explicit examples of our operators involving Hermite polynomials of v variance, Gould-Hopper polynomials and Miller-Lee polynomials are given. Also, we present some numerical examples to confirm our theoretical results.

In this paper, as a generalization of Szasz operators, a brand-new sequence of operators including the Appell polynomials of class $A^{\left(2\right)}$ is introduced. First, the convergence of this new sequence of operators is obtained, and then, some approximation results are presented by using the tools of approximation theory. In addition, an explicit example for this kind of sequence of operators containing Gould–Hopper polynomials is introduced. The error of the approximation of this new sequence of operators to a function is established.