Continuity properties of vector-valued convex functions
نویسندگان
چکیده
منابع مشابه
Extremal properties of generalized convex vector-valued functions
It is known that any local maximizer of an explicitly quasiconvex realvalued function is actually a global minimizer, whenever it belongs to the intrinsic core of the function’s domain. We show that a similar property holds for componentwise explicitly quasiconvex vector-valued functions, with respect to the optimality concepts of ideal, strong and weak efficiency. These new results are applied...
متن کاملContinuity Properties of Convex-type Set-valued Maps
K–convex, K–midconvex and (K,λ)–convex set–valued maps are considered. Several conditions implying the continuity of such maps are collected.
متن کاملSome Properties of Vector-valued Lipschitz Algebras
Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.
متن کاملHolomorphic vector-valued functions
exists. The function f is continuously differentiable when it is differentiable and f ′ is continuous. A k-times continuously differentiable function is C, and a continuous function is C. A V -valued function f is weakly C when for every λ ∈ V ∗ the scalar-valued function λ◦ f is C. This sense of weak differentiability of a function f does not refer to distributional derivatives, but to differe...
متن کاملDifferentiation of Vector-Valued Functions
This important result is listed in the theorem on the next page. Note that the derivative of the vector-valued function is itself a vector-valued function. You can see from Figure 12.8 that is a vector tangent to the curve given by and pointing in the direction of increasing values. tr t r t r f t i g t j lim t→0 f t t f t t i lim t→0 g t t g t t j lim t→0 f t t f t t i g t t g t t j lim t→0 f ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1984
ISSN: 0263-6115
DOI: 10.1017/s1446788700025453