منابع مشابه
Cone Monotone Functions: Differentiability and Continuity
We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.
متن کاملQuasi-convex Functions and Quasi-monotone Operators
The notions of a quasi-monotone operator and of a cyclically quasi-monotone operator are introduced, and relations between such operators and quasi-convex functions are established.
متن کاملDifferentiability of Cone-monotone Functions on Separable Banach Space
Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with nonempty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lips...
متن کاملEstimating Monotone Convex Functions via Sequential Shape Modification
We propose a sequential method to estimate monotone convex function that consists of: (i) monotone regression via solving a constrained least square problem and (ii) convexification of the monotone regression estimate via solving an associated constrained uniform approximation problem. We show that this method is faster than the constrained least squares (LS) method. The ratio of computation ti...
متن کاملOn a Property of Monotone and Convex Functions
G. SZEKERES We shall deal with real functions which have continuous second derivatives in some open interval (a, b), — » ^a(x) is called convex (from below) if "(x)^0 in I(<p). If <p(x) is monotone increasing and convex, and ^i(x) is monotone increasing and concave such that the range of <p(x) is contained ...
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: Pacific Journal of Mathematics
سال: 1972
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1972.43.735