Using properties of norm and inner product, we prove a new inequality for distances between five points arbitrarily given in an inner product space. Moreover, we investigate the Aleksandrov-Rassias problem by proving that if the distance 1 is contractive and the golden ratio is extensive by a mapping f , then f is a linear isometry up to translation. (2010): 51M16, 51K99, 51K05, 46C99.
Mathematics subject classification
Using familiar properties of norm and inner product, we will prove a new inequality concerning distances between each pair of n points in an inner product space, where n is an integer larger than 3. Moreover, we investigate the Aleksandrov-Rassias problem by proving that if the distance 1 is contractive and the golden ratio is extensive by a mapping f , then f is a linear isometry up to translation.
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