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A NORM INEQUALITY FOR CHEBYSHEV CENTRES | ||
Journal of Sciences, Islamic Republic of Iran | ||
مقاله 9، دوره 6، شماره 1، خرداد 1995 اصل مقاله (294.35 K) | ||
چکیده | ||
In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice function sending x to the point qT (x) with Ilx - qT (x)11= SUPfeT Ilx - dl (note that T is called remotal if such a choice function qT exists). We then use such an inequality to show that, under some restrictions, a uniquely remotal set is a singleton. Further, we show that if c is a centre of a remotal subset T of a norrned space E and x E E, then there exists a. functional f E E* such that I I f I1 I 1 and Ilx - qT (x)1I2 L I I c - q*(c)112 + 2 If (X - C) 12 - IIx - ~11 | ||
عنوان مقاله [English] | ||
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چکیده [English] | ||
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آمار تعداد مشاهده مقاله: 923 تعداد دریافت فایل اصل مقاله: 1,024 |