A function f: Rd → R is called D-convex, where D is a set of vectors in Rd, if its restriction to each line parallel to a nonzero v ∈ D is convex. The D-convex hull of a compact set A ⊂ Rd, denoted by coD(A), is the intersection of the zero sets of all nonnegative D-convex functions that are zero on A.
Motivated by problems from calculus of variations and partial differential equations, we investigate geometric properties of D-convexity. A function f: Rd→ R is.
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Motivated by problems from calculus of variations and partial differential equations, we investigate geometric properties of D-convexity.
Jun 23, 2022 · Characterize directional derivative of a convex continuous function by subdifferential · Since f is defined on A and A is open, isn't the ...
On directional convexity of harmonic mappings in the plane the harmonic convolution is defined as f ∗ F = h ∗ H + g ∗ G = z +. ∞. X n=2. anAnzn +. ∞. X n=1.
We will now prove some properties of the directional derivative as a function of the direction. Proposition 13.5 Let f\colon\mathbb{R}^n ...
Abstract. For Λ ϵ d, we say that a set A⊆ d is Λ-convex if the segment is contained in A whenever p, q ϵ A and p − q ϵ Λ. For the control system ̇ , x(0)=0ε d ...
This paper establishes further necessary conditions for optimality, by considering finite difference vectors of the type y - x(u,t), y being any point in R(t), ...
Apr 1, 2019 · A simply connected domain is said to be convex in the direction θ, 0 ≤ θ < π if every line parallel to the line through 0 and eiθ either misses ...
Mar 10, 2017 · It is shown that the convolution f*F is univalent and convex in the direction of -\mu, provided it is locally univalent and sense-preserving.