Generalized gradients of Lipschitz functionals
نویسندگان
چکیده
منابع مشابه
Generalized convex functionals
This paper studies functionals defined by multiple integrals associated to differential forms on the jet bundle of first order corresponding to some Riemannian manifolds; the domain of these functionals consists in submanifold maps satisfying certain conditions of integrability. Our idea is to give geometric properties to the domain of a functional allowing us to properly define convexity. The ...
متن کاملSuperstability of Generalized Multiplicative Functionals
LetX be a set with a binary operation ◦ such that, for each x, y, z ∈ X, either x ◦y ◦z x ◦z ◦y, or z◦ x◦y x◦ z◦y . We show the superstability of the functional equation g x◦y g x g y . More explicitly, if ε ≥ 0 and f : X → C satisfies |f x ◦ y − f x f y | ≤ ε for each x, y ∈ X, then f x ◦ y f x f y for all x, y ∈ X, or |f x | ≤ 1 √1 4ε /2 for all x ∈ X. In the latter case, the constant 1 √ 1 4...
متن کاملGeneralized Gradients and Applications
A theory of generalized gradients for a general class of functions is developed, as well as a corresponding theory of normals to arbitrary closed sets. It is shown how these concepts subsume the usual gradients and normals of smooth functions and manifolds, and the subdifferentials and normals of convex analysis. A theorem is proved concerning the differentiability properties of a function of t...
متن کاملBiseparating Maps on Generalized Lipschitz Spaces
Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F -valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uni...
متن کاملPolylogarithms, Hyperfunctions and Generalized Lipschitz Summation Formulae
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli– type polynomials. Related families of one–dimensional hyperfunctions are also constructed.
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: Advances in Mathematics
سال: 1981
ISSN: 0001-8708
DOI: 10.1016/0001-8708(81)90032-3