ON NEW BEZIER BASES WITH SCHURER POLYNOMIALS AND CORRESPONDING RESULTS IN APPROXIMATION THEORY

A new type Bezier bases with lambda shape parameters have been defined [30, Ye et al., 2010]. We slightly modify these bases to establish new Bezier bases with Schurer polynomials and lambda shape parameters. We construct a new type Schurer operators via defined new Bezier-Schurer bases. Also, we study statistical convergence properties of these operators and obtain an estimate for the rate of weighted A-statistical convergence. Moreover, we prove two Voronovskaja-type theorems including a Voronovskaja-type approximation theorem using weighted A-statistical convergence.