Differentiability of Lipschitzian mappings between Banach spaces
نویسندگان
چکیده
منابع مشابه
k LIPSCHITZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES
Let E be a real Banach space with uniformly Gâteaux differentiable norm possessing uniform normal structure. K is a nonempty bounded closed convex subset of E, and { } ( ) ... , 2 , 1 = n Tn is a sequence of − n k Lipschitzian nonexpansive mappings from K into itself such that 1 lim = ∞ → n n k and ( ) 0 1 / ≠ ∞ = n n T F ∩ and f be a contraction on K. Under sutiable conditions on sequence { },...
متن کاملFixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces
We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study...
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 کاملOn Fréchet differentiability of Lipschitz maps between Banach spaces
A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Fréchet differentiability. We show that the answer is positive for some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is...
متن کاملAsymptotic Behavior of Almost - Orbits of Reversible Semigroups of Non - Lipschitzian Mappings in Banach Spaces
Let C be a nonempty closed convex subset of a uniformly convex Banach space E with a Fr6chet differentiable norm, G a right reversible semitopological semigroup, and S {S(t) :t E G} a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself The weak convergence of an almost-orbit {u(t) :t E G} of S {S(t) :t 6 G} on C is established. Furthermore, it is show...
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: Studia Mathematica
سال: 1976
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-57-2-147-190