On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings

Details On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings

2005-01-11

arxiv.org/abs/math/0501159v2

Math. Inequal. Appl. 9 (2006), no. 3, 453-464.

Mathematics

Functional Analysis

13 pages, Added references, and title and abstract changed

Scientific paper

We prove the Cauchy-Rassias stability of linear n-inner product preserving mappings in $n$-inner product Banach spaces. We apply the Cauchy-Rassias inequality that plays an influencial role in the subject of functional equations. The inequality was introduced for the first time by Th.M.Rassias in his paper entitled: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math.Soc. 72(1978), 297-300.

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