The weighted dual functions for Wang–Bézier type generalized Ball bases and their applications

By introducing the inner-product matrix of two vector functions and using conversion matrix, explicit formulas for the dual basis functions of Wang–Bézier type generalized Ball bases (WBGB) with respect to the Jacobi weight function are given. The dual basis functions with and without boundary constraints are also considered. As a result, the paper includes the weighted dual basis functions of Bernstein basis, Wang–Ball basis and some intermediate bases. Dual functionals for WBGB and the least square approximation polynomials are also obtained.