Cheney–Sharma Type Operators on a Triangle with Straight Sides

Abstract

We consider two types of Cheney–Sharma operators for functions defined on a triangle with all straight sides. We construct their product and Boolean sum, we study their interpolation properties and the orders of accuracy and we give different expressions of the corresponding remainders, highlighting the symmetry between the methods. We also give some illustrative numerical examples.

Keywords

• Cheney–Sharma operator
• triangle
• product and Boolean sum operators
• modulus of continuity
• degree of exactness
• Peano’s theorem