Validity of the Union of Uniform Closed Balls Conjecture
Validity of the Union of Uniform Closed Balls Conjecture
Summary: A proof is provided for the union of uniform closed balls conjecture introduced in a previous paper of the authors [''Proximal smoothness and the exterior sphere condition'', J. Convex Analysis 16 501--514 (2009; Zbl 1179.49019)]; see also \textit{C. Nour}, \textit{R. J. Stern}, and \textit{J. Takche} [''The union of uniform closed balls conjecture'', Control and Cybernetics 38 (2009) 1525--1534 (2009; Zbl 1242.49038)] and [''Generalized exterior sphere conditions and \(\phi \)-convexity'', Discrete and Continuous Dynamical Systems, Serie B (to appear)]. We also provide a generalization of this conjecture to the variable radius case.
- Lebanese American University Lebanon
union of uniform closed balls property, nonsmooth analysis, Nonsmooth analysis, proximal analysis, interior and exterior sphere conditions
union of uniform closed balls property, nonsmooth analysis, Nonsmooth analysis, proximal analysis, interior and exterior sphere conditions
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