Differentiability of semigroups of Lipschitz or smooth mappings
نویسندگان
چکیده
In this note we study the differentiability with respect to time-parameter of semigroups consisting Lipschitzian or smooth self-mappings a domain in Banach space.
منابع مشابه
On Gâteaux Differentiability of Pointwise Lipschitz Mappings
Abstract. We prove that for every function f : X → Y , where X is a separable Banach space and Y is a Banach space with RNP, there exists a set A ∈ Ã such that f is Gâteaux differentiable at all x ∈ S(f) \ A, where S(f) is the set of points where f is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every K-monotone function on a separable Banach space is...
متن کاملAlmost Fréchet differentiability of Lipschitz mappings between infinite dimensional Banach spaces
We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every ǫ > 0, a point of ǫ-Fréchet differentiability. Most of these conditions are stated in terms of the moduli of asymptotic smoothness and convexity, notions which appeared in the literature under a variety of names. We prove, for example, that for ∞ > r...
متن کاملcompactifications and representations of transformation semigroups
this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...
15 صفحه اولLipschitz Properties of Convex Mappings
The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset Ω of a locally convex space X and taking values in a locally convex space Y ordered by a normal cone. One proves also equi-Lipschitz properties for pointwise bounded families of continuous convex mappings, provided the source space X is barr...
متن کاملGenerating Continuous Mappings with Lipschitz Mappings
If X is a metric space then CX and LX denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of CX modulo LX is the least cardinality of any set U \LX where U generates CX . For a large class of separable metric spaces X we prove that the relative rank of CX modulo LX is uncountable. When X is the Baire space NN, this rank is א1. A large pa...
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: Analysis and Mathematical Physics
سال: 2021
ISSN: ['1664-2368', '1664-235X']
DOI: https://doi.org/10.1007/s13324-020-00472-2