Table 2 The intervals where \(B_{n,\lambda } ( t^{2};x ) \) is convex for the corresponding values of λ and n
From: On the shape-preserving properties of λ-Bernstein operators
n | λ = 1 | λ = 1/2 | λ = −1/2 | λ = −15/16 | λ = −35/36 |
|---|---|---|---|---|---|
2 | [0,0.25] | [0.08333] | [0,0.75] | [0,0.05944] | [0,0.05881] |
3 | [0,1] | [0,1] | [0,0.92539] | [0,0.76319] | [0,0.07557] |
4 | [0,1] | [0,1] | [0,0.99254] | [0,0.84532] | [0,0.83812] |
5 | [0,1] | [0,1] | [0,1] | [0,0.89386] | [0,0.88732] |
10 | [0,1] | [0,1] | [0,1] | [0,0.97314] | [0,0.96939] |
15 | [0,1] | [0,1] | [0,1] | [0,0.98921] | [0,0.98670] |
20 | [0,1] | [0,1] | [0,1] | [0,0.99469] | [0,0.99281] |
25 | [0,1] | [0,1] | [0,1] | [0,0.99710] | [0,0.99560] |