The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>

The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>

<p/> <p>In this note, motivated by the question 1 in (Aron and Lohman, <it>Pacific J. Math.</it> 127 (1987), 209&#8211;231), we obtain an explicit formula for the <inline-formula><graphic file="1029-242X-1999-408192-i3.gif"/></inline-formula>-f...

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Bibliographic Details
Main Authors: Choi Yun Sung, Kim Sung Guen
Format: Article
Language:English
Published: SpringerOpen 1999-01-01
Series:Journal of Inequalities and Applications
Subjects:
Extreme point
&#955;-function
&#955;-property
Polynomial
Online Access:http://www.journalofinequalitiesandapplications.com/content/3/408192
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spelling doaj-bc0cb7a1577044b5b34a3b4bafdd652e2020-11-24T22:15:51ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1999-01-0119993408192The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>Choi Yun SungKim Sung Guen<p/> <p>In this note, motivated by the question 1 in (Aron and Lohman, <it>Pacific J. Math.</it> 127 (1987), 209&#8211;231), we obtain an explicit formula for the <inline-formula><graphic file="1029-242X-1999-408192-i3.gif"/></inline-formula>-function in the real space <inline-formula><graphic file="1029-242X-1999-408192-i4.gif"/></inline-formula>. From this we see that the <inline-formula><graphic file="1029-242X-1999-408192-i5.gif"/></inline-formula>-function is continuous and attained at each point of the unit ball of <inline-formula><graphic file="1029-242X-1999-408192-i6.gif"/></inline-formula>, the space of real-valued continuous 2-homogeneous polynomials on <inline-formula><graphic file="1029-242X-1999-408192-i7.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/3/408192Extreme point&#955;-function&#955;-propertyPolynomial
collection DOAJ
language English
format Article
sources DOAJ
author Choi Yun Sung
Kim Sung Guen
spellingShingle Choi Yun Sung
Kim Sung Guen
The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>
Journal of Inequalities and Applications
Extreme point
&#955;-function
&#955;-property
Polynomial
author_facet Choi Yun Sung
Kim Sung Guen
author_sort Choi Yun Sung
title The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>
title_short The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>
title_full The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>
title_fullStr The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>
title_full_unstemmed The <inline-formula><graphic file="1029-242X-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242X-1999-408192-i2.gif"/></inline-formula>
title_sort <inline-formula><graphic file="1029-242x-1999-408192-i1.gif"/></inline-formula>-function in the space <inline-formula><graphic file="1029-242x-1999-408192-i2.gif"/></inline-formula>
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 1999-01-01
description <p/> <p>In this note, motivated by the question 1 in (Aron and Lohman, <it>Pacific J. Math.</it> 127 (1987), 209&#8211;231), we obtain an explicit formula for the <inline-formula><graphic file="1029-242X-1999-408192-i3.gif"/></inline-formula>-function in the real space <inline-formula><graphic file="1029-242X-1999-408192-i4.gif"/></inline-formula>. From this we see that the <inline-formula><graphic file="1029-242X-1999-408192-i5.gif"/></inline-formula>-function is continuous and attained at each point of the unit ball of <inline-formula><graphic file="1029-242X-1999-408192-i6.gif"/></inline-formula>, the space of real-valued continuous 2-homogeneous polynomials on <inline-formula><graphic file="1029-242X-1999-408192-i7.gif"/></inline-formula>.</p>
topic Extreme point
&#955;-function
&#955;-property
Polynomial
url http://www.journalofinequalitiesandapplications.com/content/3/408192
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