Journal of Convex Analysis 26 (2019), No. 2, 617--633
Copyright Heldermann Verlag 2019
Sets with the Unique Footpoint Property and φ-Convex Subsets of Riemannian Manifolds
Mohamad R. Pouryayevali
Department of Mathematics, University of Isfahan, Isfahan, Iran
pourya@math.ui.ac.ir
Hajar Radmanesh
Department of Mathematics, University of Isfahan, Isfahan, Iran
h.radmanesh@sci.ui.ac.ir
The concepts of φ-convexity and prox-regularity for sets are studied in the framework of finite-dimensional Riemannian manifolds. We prove that the two concepts coincide and these sets are contained in the class of sets with the unique footpoint property. Then by using a characterization of elements of proximal normal cone, we show that under certain conditions a set with the unique footpoint property is a φ-convex set.
Keywords: Phi-convex sets, prox-regular sets, sets with the unique footpoint property, nonsmooth analysis, Riemannian manifolds.
MSC: 58C20, 58C06, 49J52
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