This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) I...This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) If f(P) satisfies Lipschitz continuous condition, i. e. f(P)∈Lip4α, then the corresponding Bernstein Bezier net fn∈LipAsecαψα, here ψ is the half of the largest angle of triangle T; (2) If Bernstein Bezier net fn∈ LipBα, then its elevation Bezier net Efn∈LipBα; and (3) If f(P)∈Lipαa, then the corresponding Bernstein polynomials Bn(f;P)∈LipAsecαψα, and the constant Asecαψ best in some sense.展开更多
基金Supported by NSF and SF of National Educational Committee
文摘This paper proved the following three facts about the Lipschitz continuous property of Bernstein polynomials and Bezier nets defined on a triangle: suppose f(P) is a real valued function defined on a triangle T, (1) If f(P) satisfies Lipschitz continuous condition, i. e. f(P)∈Lip4α, then the corresponding Bernstein Bezier net fn∈LipAsecαψα, here ψ is the half of the largest angle of triangle T; (2) If Bernstein Bezier net fn∈ LipBα, then its elevation Bezier net Efn∈LipBα; and (3) If f(P)∈Lipαa, then the corresponding Bernstein polynomials Bn(f;P)∈LipAsecαψα, and the constant Asecαψ best in some sense.
