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<p>In this paper, we introduce the notions called uniformly strongly convex and nearly U-convex Banach spaces, and investigate their properties. We characterize local uniform rotundity (LUR) in terms of these two notions. Uniform strong convexity is stronger than the well-known concept of strong convexity but weaker than LUR. We also consider notions that are weaker than uniform strong convexity.</p>

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Uniformly Strongly Convex Banach Spaces

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • P. Shunmugaraj,
  • Constantin Zălinescu

摘要

In this paper, we introduce the notions called uniformly strongly convex and nearly U-convex Banach spaces, and investigate their properties. We characterize local uniform rotundity (LUR) in terms of these two notions. Uniform strong convexity is stronger than the well-known concept of strong convexity but weaker than LUR. We also consider notions that are weaker than uniform strong convexity.