The r-monotonicity of generalized Bernstein polynomials
2012 ◽
Vol 55
(3)
◽
pp. 797-807
Keyword(s):
AbstractLet f ∊ C[0, 1] and let the Bn(f, q; x) be generalized Bernstein polynomials based on the q-integers that were introduced by Phillips. We prove that if f is r-monotone, then Bn(f, q; x) is r-monotone, generalizing well-known results when q = 1 and the results when r = 1 and r = 2 by Goodman et al. We also prove a sufficient condition for a continuous function to be r-monotone.
2004 ◽
Vol 44
(1)
◽
pp. 63-78
◽
2005 ◽
Vol 178
◽
pp. 55-61
◽
1999 ◽
Vol 42
(2)
◽
pp. 403-413
◽
2002 ◽
Vol 116
(1)
◽
pp. 100-112
◽
2019 ◽
Vol 56
(1)
◽
pp. 22-44
Keyword(s):
2019 ◽
Vol 8
(10)
◽
pp. 308-313