The modulus of convexity is a quantitative measure that reflects the degree of convexity of a normed space. It is defined as a function that captures how 'far' from being a linear space the normed space is, particularly focusing on how the distance between points can be controlled in terms of their convex combinations. This concept connects deeply to duality mappings as it provides insights into the geometric properties of functional spaces, helping to understand their structure and behavior.
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