On extensions of Lipschitz functions

Extensions of Lipschitz functions and Grothendieck's BAP

A metric compact space M is seen as the closure of the union of a sequence (Mn) of finite n-dense subsets. Extending to M (up to a vanishing uniform distance) Banach-space valued Lipschitz functions defined on Mn, or defining linear continuous near-extension operators for real-valued Lipschitz functions on Mn, uniformly on n is shown to be equivalent to the bounded approximation property for th...

Rotund Norms, Clarke Subdifferentials and Extensions of Lipschitz Functions

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

Perturbed Smooth Lipschitz Extensions of Uniformly Continuous Functions on Banach Spaces

We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have Cp-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y ∩U → R and every ε > 0, there exists a Cp-smooth Lipschitz function F : X → R such that |F (y)− f(y)| ≤ ε for every y ∈ Y ∩U . If we are given a separable subspace Y o...

On fully operator Lipschitz functions

Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions...