On n-collinear elements and Riesz theorem

Volume 9, Issue 5, pp 3066--3073 http://dx.doi.org/10.22436/jnsa.009.05.98

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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.

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Keywords

• n-normed space
• invex set
• linearly dependent
• collinear elements.

MSC

•  15A39.

References

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