Lipschitz Continuity of Convex FunctionsConvex functionLipschitz continuityCalmnessSubdifferentialNormal coneMoreau envelope functionWe provide some necessary and sufficient conditions for a proper lower semico
convex hullWe study continuity and regularity of convex extensions of functions from a compact set $C$ to its convex hull $K$. We show that if $C$ contains the relative boundary of $K$, and $f$ is a continuous convex function on $C$, then $f$ extends to a continuous convex ...
respectively. It is rather simple with an elementary proof, but with it we will draw a whole series of useful conclusions. In Sect.2it is shown thatandare measurable and semi-continuous. On the setof all convex functions with exactly one minimizer the...
13.On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space. 另外,本文利用邻域的"平移"方法,给出了定义赋范线性空间的凸集上的次凸泛函连续性的简捷证明。 声明:以上例句、词性分类...
13.On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space. 13.另外,本文利用邻域的"平移"方法,给出了定义在赋范线性空间内的凸集上的次凸泛函连性的简捷证明。 用户正在搜索 inte...
Examples and Properties of Absolutely Continuous FunctionsEvery convex function and every continuously differentiable function is absolutely continuous [3].Given a real-valued absolutely continuous function, the following properties hold [6]:cf, where c ∈ ℝ f + g fg 1/f, if f(x) ≠ 0 for...
In the geometries of stratified groups, we show that H-convex functions locally bounded from above are locally Lipschitz continuous and that the class of v-convex functions exactly corresponds to the class of upper semicontinuous H-convex functions. As a consequence, v-convex functions are locally...
Therefore, for any compact set K, the family of density functions (pt(x, ·))x∈K is uniformly integrable with respect to µt, see e.g. [24, Theorem 16.8]. Consequently, there exists an even, increasing and convex function Φt : R → R+ with Φt(0) = 0 and STRONG FELLER ...
1.The Singularity and Absolute Continuity of Fuzzy Measures;FUZZY测度的奇异性与绝对连续性 2.The characteritation of a Banach space no containing copy of C_0 has been given by the equivalence ofabsolute continuityof functions.通过取值于 Banach空间中两种绝对连续函数的等价性刻画了不含c_0BanaCh空间...
摘要: Order estimates are obtained for the approximations of the classes \( B_{p,heta }^\Omega \) of periodic functions of two variables in the space L q by operators of orthogonal projection and by linear operators satisfying certain conditions....