A Characterization of Inner Product Spaces Related to the Skew-Angular Distance

TL;DR

This paper introduces a refined triangle inequality in normed spaces and characterizes inner product spaces using the skew-angular distance, advancing the understanding of geometric properties in functional analysis.

Contribution

It provides a new refinement of the triangle inequality and offers a simple characterization of inner product spaces through the skew-angular distance.

Findings

Refined triangle inequality in normed spaces

Characterization of inner product spaces using skew-angular distance

Simplified geometric criteria for inner product spaces

Abstract

A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.