Currently displaying 1 – 13 of 13

Showing per page

Order by Relevance | Title | Year of publication

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz — 2009

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: 1 . if M is a linear manifold, then (M) contains convex functions, 2 . (·) is invariant under diffeomorphisms, 3 . each f ∈ (M) is differentiable on a dense G δ -set, is investigated.

On a globalization property

Stefan Rolewicz — 1993

Applicationes Mathematicae

Let (X,τ) be a topological space. Let Φ be a class of real-valued functions defined on X. A function ϕ ∈ Φ is called a local Φ-subgradient of a function f:X → ℝ at a point x 0 if there is a neighbourhood U of x 0 such that f(x) - f( x 0 ) ≥ ϕ(x) - ϕ( x 0 ) for all x ∈ U. A function ϕ ∈ Φ is called a global Φ-subgradient of f at x 0 if the inequality holds for all x ∈ X. The following properties of the class Φ are investigated: (a) when the existence of a local Φ-subgradient of a function f at each point implies...

Equations in linear spaces

CONTENTSPreface...................... 5Acknowledgment...................... 7PART A. LINEAR OPERATORS IN LINEAR SPACESCHAPTER I. Operators with a finite and semifinite dimensional characteristic........ 25CHAPTER II. Algebraic and almost algebraic operators........ 65CHAPTER III. Φ_Ξ-operators........ 90CHAPTER IV. Determinant theory of Φ_Ξ-operators........ 102PART B. LINEAR OPERATORS IN LINEAR TOPOLOGICAL SPACESCHAPTER I. Linear topological and linear metric space........ 115CHAPTER II. Continuous...

Page 1

Download Results (CSV)