Sz´asz-Beta operators linking general-Appell Polynomials

Abstract

This manuscript associates with a study of general-Appell
Polynomials. In this research work, we construct a new sequence of
Sz´asz-Beta type operators via general-Appell Polynomials to discuss approximation
properties for the Lebesgue integrable functions (L1[0,∞)).
Further, estimates in view of test functions and central moments are
studied. Next, rate of convergence is discussed with the aid of Korovkin
theorem and Voronovskaja type theorem. Moreover, direct approximation
results in terms of modulus of continuity of first and second order,
Peetre’s K-functional, Lipschitz type space, and the rth order Lipschitz
type maximal functions are investigated. In subsequent section,
we present weighted approximation results and statistical approximation
theorems are discussed.