ON STRICTLY n-CONVEX NORMED LINEAR SPACES

Lin, C.-S.

doi:10.1515/dema-1993-3-419

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2023

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“…By letting n → ∞ in the above inequality we obtain x − y = 0, hence x = y and assertion 1 0 is proved. The fact that assertion 2 0 follows from 1 0 was proved by Lin [22].…”

Section: Resultsmentioning

confidence: 91%

Inequalities That Imply the Norm of a Linear Space Is Induced by an Inner Product

Rădulescu,

Bencze

2023

Mathematics

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The aim of this paper is to investigate when a linear normed space is an inner product space. Several conditions in a linear normed space are formulated with the help of inequalities. Some of them are from the literature and others are new. We prove that these conditions are equivalent with the fact that the norm is induced by an inner product. One of the new results is the following: in an inner product space, the sum of opposite edges of a tetrahedron are the sides of an acute angled triangle. The converse of this result holds also. More precisely, this property characterizes inner product spaces. Another new result is the following: in a tetrahedron, the sum of squares of opposite edges are the lengths of a triangle. We prove also that this property characterizes inner product spaces. In addition, we give simpler proofs to some theorems already known from the publications of other authors.

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“…By letting n → ∞ in the above inequality we obtain x − y = 0, hence x = y and assertion 1 0 is proved. The fact that assertion 2 0 follows from 1 0 was proved by Lin [22].…”

Section: Resultsmentioning

confidence: 91%

Inequalities That Imply the Norm of a Linear Space Is Induced by an Inner Product

Rădulescu,

Bencze

2023

Mathematics

View full text Add to dashboard Cite

show abstract

ON STRICTLY n-CONVEX NORMED LINEAR SPACES

Cited by 1 publication

References 6 publications

Inequalities That Imply the Norm of a Linear Space Is Induced by an Inner Product

Inequalities That Imply the Norm of a Linear Space Is Induced by an Inner Product

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