Uniform convexity and the splitting problem for selections

Abstract

We continue to investigate cases when the Repovš-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.

References in corpus (3)

• On Some Estimates for Projection Operator in Banach Space
• On the splitting problem for selections
• Hereditary invertible linear surjections and splitting problems for selections

Cited by in corpus (7)

• Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
• Local characterization of strongly convex sets
• Continuous selections of multivalued mappings
• Curvature of Feasible Sets in Offline and Online Optimization
• Weakly convex sets and modulus of nonconvexity
• Polyhedral approximations of strictly convex compacta
• An extension of the Polyak convexity principle with application to nonconvex optimization