Approximation by Bézier variant of the Baskakov- Kantorovich operators in the case $0 \lt\alpha\lt 1$

Abstract

The present paper deals with the approximation of B\'{e}zier variants of Baskakov-Kantorovich operators $V_{n,\alpha}^{*}$ in the case $0\lt \alpha\lt 1$. Pointwise approximation properties of the operators $V_{n,\alpha}^{*}$ are studied. A convergence theorem of this type approximation for locally bounded functions is established. This convergence theorem subsumes the approximation of functions of bounded variation as a special case.