Ismail-May-Kantorovich operators preserving affine functions

Abstract

We introduce here a modification of the Ismail-May operators, preserving affine function and estimate the order of approximation with the help of classical approach viz. the second order modulus of continuity, and the Peetre’s $K$-functional. Further, we provide the convergence estimates for the  differences of Ismail-May operators and its Kantorovich variants. In the end, the convergence of the operators have been depicted through illustrative graphics.