Szász-integral operators linking general-Appell polynomials and approximation
Nadeem Rao, Mohammad Farid, Nand Kishor Jha
Abstract
This manuscript is associated with a study of general Appell polynomials. In this research work, we introduced a new sequence of Szász-Integral type of sequence of operators via general-Appell polynomials to discuss approximation properties for Lebesgue integrable functions $ (L^p[0, \infty)) $. In addition, estimates are studied in view of test functions and central moments. Next, the convergence rate is discussed using the Korovkin theorem and a Voronovskaja-type theorem. Moreover, direct approximation results via modulus of continuity of first and second order, Peetre's K-functional, Lipschitz type space, and the $ r^{th} $ order Lipschitz type maximal functions are investigated. In the following section, we present weighted approximation results, and statistical approximation theorems are discussed.