The main goal of this research is to obtain several approximation properties of Kantorovich variant Sz?sz-Chlodowsky operators based on 2D Appell Polynomials. We provide a connection between weighted B-statistical convergence (WBSC) and the rate of WBSC concepts and approximation theory. We also prove a Voronovskaja theorem related to WBSC. Finally, we consider certain examples and discuss the advantages of proposed operators via certain numerical results.

This study investigates the shape-preserving characteristics of 𝜆-Schurer operators, a class of operators derived from a modified version of the classical Schurer bases by incorporating a shape parameter 𝜆. The primary focus is on understanding how these operators maintain the geometric features of the functions they approximate, which is crucial in fields like computer graphics and geometric modelling. By examining the fundamental properties and the divided differences associated with 𝜆-Schurer bases, we derive vital results that confirm the operators’ capability to preserve essential shape attributes under various conditions. The findings have significant implications for the application of these operators in computational analysis and other related areas, providing a solid foundation for future research.