A Whitney extension theorem for functions taking values in scales of Banach spaces

Extension of a theorem of Whitney

It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triangulation.

A FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

An Extension of Elton’s `1 Theorem to Complex Banach Spaces

Let ε > 0 be sufficiently small. Then, for θ = 0.225 √ ε, there exists δ := δ(ε) < 1 such that if (ei) n i=1 are vectors in the unit ball of a complex Banach space X which satisfy

A “coboundary” Theorem for Sums of Random Variables Taking Their Values in a Banach Space

For a given metric space (S, d), let us use the term “standard σ-field” to denote the σ-field S of subsets of S generated by the open balls (in the metric d). A function f : S×S×S× . . .→ S is “measurable” (with respect to S) if for every set A ∈ S one has that f−1(A) is a member of S×S×S×. . . , the product σ-field on S × S × S × . . . . Suppose B is a separable real Banach space. Suppose (Ω,F...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition