A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α

Abstract

The objective of this paper is to construct univariate and bivariate blending type $\alpha$-Schurer–Kantorovich operators depending on two parameters $\alpha \in \left[\mathrm{0,1}\right]$ and $\rho >0$ to approximate a class of measurable functions on $\left[\mathrm{0,1}+q\right],q>0$. We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetre’s $K$-functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.