In this paper we change the several important theorems in Calculus, about these theorems. angle of view to consider the connections among and give alternative proofs and new implications
We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, l...We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, lim ||fn - f0|| = 0. If and only if θ w-limsup Hn Ho It simplifies the related results in [1].展开更多
文摘In this paper we change the several important theorems in Calculus, about these theorems. angle of view to consider the connections among and give alternative proofs and new implications
文摘We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, lim ||fn - f0|| = 0. If and only if θ w-limsup Hn Ho It simplifies the related results in [1].
