1) approximately additive mappings
近似可加映射
1.
We first introduce functional index A_r(-) to study approximately additive mappings.
我们通过引进泛函指标A_Υ(·)来刻画近似可加映射,证明了对于从群到Banach空间内的任一个映射f,只要A_Υ(f)是有界的,那么f在Hyers和Ulam意义下就是稳定的。
2) Approximately derivable map
近似可导映射
3) approximately multiplicative mappings
近似可乘映射
4) η-proximal mapping
η-近似映射
5) J-proximal mapping
J-近似映射
1.
In this paper, a new concept of a J-proximal mapping of a proper sub-dif-ferentiable functional (which may not be convex) on Banach spaces is introduced.
在Banach空间上引入恰当次可微泛函(可以不是凸的)的J-近似映射的新概念。
6) additive map
可加映射
1.
Suppose thatΦ:A→A is an additive map and m,n are positive integers.
设Φ:■→■是可加映射。
2.
Using the additivity of the matrix,it is proved that every additive map preserving the lattices of invariant subspaces is of the form:Φ(A)=αA+φ(A)I(A∈Tn),where α is a nonzero scalar,φ:TnF is an additive map and I∈Tn is an identity.
利用矩阵的可加性,证明了Tn上的每一个保不变子空间格的可加映射Φ为:Φ(A)=αA+φ(A)I(A∈Tn),其中α是非零常数,φ∶Tn→F是可加映射,I∈Tn是单位算子。
3.
The form of each additive map φ:M→B(X) is proved that if there exist nonzero real m and n such that (m+n)φ(A2)-mAφ(A)-nφ(A)A ∈FI holds for all A ∈ M, then φ(A)=λA , where λ ∈F.
证明了若可加映射φ:M→B(X)满足A∈M,非零实数m和n,有(m+n)φ(A2)-mAφ(A)-nφ(A)A∈FI。
补充资料：博尔加坦加
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