Characterizing of Inner Product Spaces by the Mapping n_x,y

2015/02/08 by Hossein Dehghan, Dehghan, Hossein
Computer Science · Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.CA #math.FA

paper · pdf · doi:10.48550/arxiv.1502.02250

arxiv created 2015/02/08 · openalex publication_date 2015/02/08 · arxiv updated 2015/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the vectors x and y in a normed linear spaces X, the mapping n_x,y: ℝ→ ℝ is defined by n_x,y(t)=‖x+ty‖. In this note, comparing the mappings n_x,y and n_y,x we obtain a simple and useful characterization of inner product spaces.

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