Approximations: Modified Sz´asz-Beta operators via general-Appell Polynomials

Abstract

We present a new sequence of modified Sz´asz-Beta type sequence of operators via general-Appell Polynomials to investigate the approximation properties of Lebesgue integrable functions (L1[0, ∞)). In addition, we study estimates in view of test functions and central moments. Next, convergence rate is discussed using the Korovkin theorem and 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 rth order Lipschitz type maximal functions are investigated. In subsequent section, weighted approximation results and statistical approximation theorems are discussed.