  In the present manuscript, we present a new sequence of operators, $i.e.$,
$\alpha$-Bernstein-Schurer-Kantorovich operators depending on two parameters
$\alpha\in[0,1]$ and $\rho>0$ for one and two variables to approximate
measurable functions on $[0: 1+q], q>0$. Next, we give basic results and
discuss the rapidity of convergence and order of approximation for univariate
and bivariate of these sequences in their respective sections. Further,
Graphical and numerical analysis are presented. Moreover, local and global
approximation properties are discussed in terms of first and second order
modulus of smoothness, Peetre's K-functional and weight functions for these
sequences in different spaces of functions.
