Convergence properties related to B\'{e}zier type of $\lambda$-Bernstein Kantorovich shifted knots operators

Abstract

In this article, we introduce the $L_p$-spaces and create the Kantorovich-type operators of Schurer $\lambda$-Bernstein-B\'{e}zier basis functions, starting with shifted knots polynomials. We describe the convergence of our novel operators in the Lebesgue spaces and the continuous function space for any $1 \leq p<\infty$. The central moments for these operators are determined by computing the test functions.   We then examine the properties of the Korovkin's type approximation with modulus of continuity of order one and two. We also derive the convergence theorems for these new operators using Peetre's $K$-functional and the fundamental conditions of Lipschitz continuous functions. Several direct approximation theorems are also derived by us. In last we given a numerical example with a graphical analysis.