目的为克服Lagrange插值多项式不能对任意连续函数都一致收敛的问题,构造了一类二元乘积型三角插值多项式算子使得该算子在全平面上能够一致收敛到每个以2π为周期的二元连续函数。方法通过对Lagrange插值三角多项式的平移与组合,在已...目的为克服Lagrange插值多项式不能对任意连续函数都一致收敛的问题,构造了一类二元乘积型三角插值多项式算子使得该算子在全平面上能够一致收敛到每个以2π为周期的二元连续函数。方法通过对Lagrange插值三角多项式的平移与组合,在已有成果的基础上做了推广,构造了一类形式较为广泛的二元乘积型三角插值多项式Tmn(f;x,y)=sum from κ=0 to 2m sum from l=0 to 2n f(xκ,yl)mακ(x)mβl(x),进而讨论了该算子的逼近性质。结果/结论证明了该算子在全平面上一致收敛到任意以2π为周期的二元连续函数,并且对C2sπ,r,2π(s≤α,r≤β)函数类的逼近均达到最佳收敛阶,即,当f(x,y)∈Cs2,πr,2π,s≤α,r≤β,成立|Tmn(f;x,y)-f(x,y)|=O{Em*n(f)+1/m^sω(~sf/x^s;1/m,0)+r/n^1ω(~rf/y^r;0,1/n)+1/m^s 1/n^rω(^(s+r)f/x^sy^r;1/m,1/n)}。展开更多
With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it...With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.展开更多
文摘目的为克服Lagrange插值多项式不能对任意连续函数都一致收敛的问题,构造了一类二元乘积型三角插值多项式算子使得该算子在全平面上能够一致收敛到每个以2π为周期的二元连续函数。方法通过对Lagrange插值三角多项式的平移与组合,在已有成果的基础上做了推广,构造了一类形式较为广泛的二元乘积型三角插值多项式Tmn(f;x,y)=sum from κ=0 to 2m sum from l=0 to 2n f(xκ,yl)mακ(x)mβl(x),进而讨论了该算子的逼近性质。结果/结论证明了该算子在全平面上一致收敛到任意以2π为周期的二元连续函数,并且对C2sπ,r,2π(s≤α,r≤β)函数类的逼近均达到最佳收敛阶,即,当f(x,y)∈Cs2,πr,2π,s≤α,r≤β,成立|Tmn(f;x,y)-f(x,y)|=O{Em*n(f)+1/m^sω(~sf/x^s;1/m,0)+r/n^1ω(~rf/y^r;0,1/n)+1/m^s 1/n^rω(^(s+r)f/x^sy^r;1/m,1/n)}。
文摘With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.
