On n-collinear elements and Riesz theorem
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Authors
Wasfi Shatanawi
- Department of Mathematics, Hashemite University, P. O. Box 150459, Zarqa 13115, Jordan.
Mihai Postolache
- Department of Mathematics and Informatics, University Politehnica of Bucharest, Bucharest, 060042, Romania.
Abstract
In this paper, we prove that the n-collinear elements \(x_1; x_2; : ... ; x_n; u\) satisfy some special relations in an
n-normed space X. Further, we prove that \(u =\frac{ x_1+...+x_n}{n}\) is the only unique element in the n-normed space
X such that \(x_1; x_2; ... ; x_n; u\) are n-collinear elements in X satisfying some specified inequalities. Moreover,
we prove that the Riesz theorem holds when X is a linear n-normed space.
Share and Cite
ISRP Style
Wasfi Shatanawi, Mihai Postolache, On n-collinear elements and Riesz theorem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3066--3073
AMA Style
Shatanawi Wasfi, Postolache Mihai, On n-collinear elements and Riesz theorem. J. Nonlinear Sci. Appl. (2016); 9(5):3066--3073
Chicago/Turabian Style
Shatanawi, Wasfi, Postolache, Mihai. "On n-collinear elements and Riesz theorem." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3066--3073
Keywords
- n-normed space
- invex set
- linearly dependent
- collinear elements.
MSC
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