Tangent metric spaces to starlike sets on the plane

Dovgoshey O., ABDULLAYEV F., Küçükaslan M.

Journal of Nonlinear and Convex Analysis, vol.14, no.3, pp.551-581, 2013 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2013
  • Journal Name: Journal of Nonlinear and Convex Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.551-581
  • Keywords: Metric spaces, Tangent space to convex sets, Tangent space to starlike sets, Tangent spaces to metric spaces
  • Uşak University Affiliated: No

Abstract

Let A ⊆ ℂ b e a starlike set with a center a. We prove that every tangent space to A at the point o is isometric to the smallest closed cone, with the vertex a, which includes A. A partial converse to this result is obtained. The tangent space to convex sets is also discussed. © 2013.