valuedfunction MSC2010:26A24,26E60 1.Introduction LetI⊂Rbeaninterval.RecallthatafunctionM:I 2 →Rissaidtobeamean inIif,forallx,y∈I, min(x,y) M(x,y) max(x,y). AmeanMinIiscalledstrictiftheseinequalitiesaresharpwheneverx=y,and
Vector-ValuedFunctions131向量值函数
As an application we derive weak-strong principles for continuously partially differentiable functions of finite order and vector-valued versions of Blaschke’s convergence theorem for several spaces.Similar content being viewed by others Taylor’s Theorem, the Inverse Function Theorem and the Implicit ...
Since weighted spaces of continuously partially differentiable vector-valued functions will serve as our standard examples, we recall the definition of the spaces Ck(Ω,E). A function f:Ω→E on an open set Ω⊂Rd to an lcHs E is called continuously partially differentiable (f is C1) if ...
A real-valued function F(x) may be defined in a vector form as follows: (1.10)F(x)=[F1,F2,…,Fm],F:Rn→Rm where Fi, i = 1,…,m the elements of the matrix F are real-valued functions of real numbers. If F(x) is a scalar matrix, its gradient is defined as follows: ...
On the computation of an element of Clarke generalized Jacobian for a vector-valued max function The Globalization of Stock Markets and Convergence in Corporate The Convergence of International Trade and Investment… 东南亚跨国有组织犯罪的欺诈报告 Transnational Organized Crime and the Convergence of Cyber...
Function transformations include, but are not limited to the well known technique of linear function transformations .A function transformation simply means a mathematical operation through which a real or complex -valued function f is transformed into another function F ,or into a sequences of ...
It is well known that a real-valued function f has a saddle point (x0, y0) ∈ A × B if and only if (1.1) holds (see [3]). Recently, many researchers, such as Nieuwenhuis [4], Ferro [7,8], Tanaka [5,6], Chen [9], Li and Wang [10], Shi and Ling [11], Chang, ...
whereis a permutation on,Lis a surjective linear (n/2,m)-function, andgis an arbitrary (n/2,m)-function. With the Nyberg’s bound, one can interpret the bent property of a vectorial function as follows. An (n,m)-functionFwithis vectorial bent, if it has the maximum number of bent...
This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence an...