A new kind of Bi-variate $ \lambda $ -Bernstein-Kantorovich type operator with shifted knots and its associated GBS form

<p style='text-indent:20px;'>In this paper, we introduce a bi-variate case of new kind <inline-formula><tex-math id="M1">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-Bernstein-Kantorovich type operator with shifted knots defined by Rahman et al. [<xref ref-type="bibr" rid="b31">31</xref>]. The rate convergence the operators is obtained in terms complete and partial moduli continuity. Next, give an error estimate approximation function Lipschitz class establish Voronovskaja theorem. Also, define associated GBS(Generalized Boolean Sum) study degree Bögel continuous differentiable functions these aid mixed modulus smoothness. Finally, show their GBS for certain illustrative graphics tables using MATLAB algorithms.</p>