Vol. 91, No. 1, 1980

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ISSN: 0030-8730
A quantitative version of Krasnosel’skiĭ ’s theorem in R2

Marilyn Breen

Vol. 91 (1980), No. 1, 31–37
Abstract

This work concerns a quantitative version of Krasnosel’skii’s theorem in R2, and the following result is obtained: Let S be a nonempty compact subset of R2 having n points of local nonconvexity. Then the kernel of S contains an interval of radius 𝜀 > 0 if and only if every f(n) = max{4,2n} points of S see via S a common interval of radius 𝜀. The number f(n) in the theorem is best possible for every n 1.

Mathematical Subject Classification 2000
Primary: 52A10
Secondary: 52A35
Milestones
Received: 18 September 1979
Revised: 15 February 1980
Published: 1 November 1980
Authors
Marilyn Breen