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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 ν variance, Gould-Hopper polynomials and Miller-Lee polynomials are given. Also, we present some numerical examples to confirm our theoretical results.

This paper deals with the analysis of the orthogonality of a monic polynomial sequence fQ n } n$0 defined as a linear combination of a sequence of monic orthogonal polynomials fP n } n$0 withwhere r n -0 for n $ 3. Moreover, we obtain the relation between the corresponding linear functionals as well as an explicit expression for the sequence of monic orthogonal polynomials fQ n } n$0 . We obtain the connection between the Jacobi matrices associated with fP n } n$0 and fQ n } n$0 , respectively, by using an LU factorization. Some special cases of the above type relation are analysed.

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The purpose of this paper is to find the characterization of the Sheffer polynomial sets satisfying the d-orthogonality conditions. The generating function form of these polynomial sets is given in Theorem 2.2. As applications of the Theorem 2.2, we revisit the d-orthogonal polynomial sets exist in the literature and discover new d-orthogonal polynomial sets. Moreover, we obtain the d-dimensional functional vector ensuring the d-orthogonality of these new polynomial sets.

In this contribution, we define a new operator sequence which contains analytic functions. Using approximation techniques found by Korovkin, some results are derived. Moreover, a generalization of this operator sequence called Kantorovich type generalization is introduced.