کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6418143 | 1339322 | 2015 | 6 صفحه PDF | دانلود رایگان |
Brodskii and Milman proved that there is a point in C(K), the set of all Chebyshev centers of K, which is fixed by every surjective isometry from K into K whenever K is a nonempty weakly compact convex subset having normal structure in a Banach space. Motivated by this result, Lim et al. raised the following question namely “does there exist a point in C(K) which is fixed by every isometry from K into K?”. In fact, Lim et al. proved that “if K is a nonempty weakly compact convex subset of a uniformly convex Banach space, then the Chebyshev center of K is fixed by every isometry T from K into K”. In this paper, we prove that if K is a nonempty weakly compact convex set having normal structure in a strictly convex Banach space and F is a commuting family of isometry mappings on K then there exists a point in C(K) which is fixed by every mapping in F.
Journal: Journal of Mathematical Analysis and Applications - Volume 422, Issue 2, 15 February 2015, Pages 880-885