Extension of some Cheney-Sharma type operators to a triangle with one curved side

TL;DR

This paper extends Cheney-Sharma type operators to a triangle with a curved side, analyzing their properties, accuracy, and providing illustrative examples.

Contribution

It introduces new extensions of Cheney-Sharma operators to curved-sided triangles, including their product, Boolean sum, and interpolation properties.

Findings

Operators' interpolation properties are established

Orders of accuracy are analyzed

Explicit remainder expressions are provided

Abstract

We extend some Cheney-Sharma type operators to a triangle with one curved side. We construct their product and Boolean sum, we study their interpolation properties, the orders of accuracy and we give different expressions of the corresponding remainders. We also give some illustrative examples.