Abstract
We construct the Schurer-Kantorovich operators depending on the shape parameter alpha is an element of [0, 1] which we called alpha-Schurer-Kantorovich operators, and estimate their moments and central moments. We discuss the uniform convergence as well as the rate of convergence in terms of modulus of smoothness and Lipschitz-type functions, and other related results for our new aforementioned operators. Further, we construct the bivariate a-Schurer-Kantorovich operators and investigate the degree of convergence with the help of Lipschitz class for bivariate function. Moreover, we discuss the approximation behaviors of bivariate alpha-Schurer-Kantorovich operators for functions having continuous partial derivatives. Statement: We constructed the alpha-Schurer-Kantorovich operators and established several approximation results. Our operators coincide with a-Bernstein-Kantorovich operators (for nu = 0), Schurer- Kantorovich operators (for alpha = 1), and Bernstein- Kantorovich operators (for alpha = 1 and nu = 0) which means that our operator is stronger than existing in the literature. Thus, we believe that the new operator will open new vistas in this field.