Differentiability of distance function and the proximinal condition implying convexity
نویسندگان
چکیده
منابع مشابه
Differentiability of Distance Functions and a Proximinal Property Inducing Convexity
In a normed linear space X, consider a nonempty closed set K which has the property that for some r > 0 there exists a set of points xo € X\K, d(xoK) > r, which have closest points p(xo) € K and where the set of points xo — r((xo — p(xo))/\\xo — p(zo)||) is dense in X\K. If the norm has sufficiently strong differentiability properties, then the distance function d generated by K has similar dif...
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ژورنال
عنوان ژورنال: The Journal of Analysis
سال: 2020
ISSN: 0971-3611,2367-2501
DOI: 10.1007/s41478-020-00259-5