Hermite polynomials linking Szász–Durrmeyer operators

• Published in: Computational & applied mathematics Vol. 43; no. 4
• Main Authors: Ayman-Mursaleen, Mohammad, Heshamuddin, Md, Rao, Nadeem, Sinha, Brijesh Kumar, Yadav, Avinash Kumar
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Approximation; Bivariate analysis; Computational Mathematics and Numerical Analysis; Convergence; Gamma function; Hermite polynomials; Mathematical analysis; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Operators (mathematics); Sequences; Smoothness; Theorems; Szász operators; 41A35; 41A25; 41A36; 41A30; Hermite polynomials; Rate of convergence; Order of approximation; Modulus of smoothness
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-024-02752-0

The aim of present article is to introduce the Szász-integral type sequences of operators in terms of Hermite polynomials and gamma function. Further, we calculate some estimates at test functions and central moments. Moreover, we discuss uniform convergence theorem and order of approximation via Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in view of Peetre’s K -functional, second order modulus of smoothness and Lipschitz type space. Lastly, bivariate version of these sequences of operators are introduced. Moreover, their rate of convergence and order of approximation are investigated.