On the Cauchy--Rassias Inequality and Linear n-Inner Product Preserving Mappings
Choonkil Baak, Hahng-Yun Chu, Mohammad Sal Moslehian
Abstract
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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