Open problems in theory of metric linear spaces
How to define "convex functions" on differentiable manifolds
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
On a generalization of the Dvoretzky-Rogers theorem
Paraconvex analysis
On σ-porous and Φ-angle-small sets in metric spaces
On a globalization property
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 if there is a neighbourhood U of such that f(x) - f() ≥ ϕ(x) - ϕ() for all x ∈ U. A function ϕ ∈ Φ is called a global Φ-subgradient of f at 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...
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On bounded sets in F-spaces
Remarks on the existence of the Riemann-Stieltjes integral
Coefficient of orthogonal convexity of some Banach function spaces
We study orthogonal uniform convexity, a geometric property connected with property (β) of Rolewicz, P-convexity of Kottman, and the fixed point property (see [19, [20]). We consider the coefficient of orthogonal convexity in Köthe spaces and Köthe-Bochner spaces.
Some properties of the space (s)
On approximations of functions on metric spaces
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...
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