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<p>We investigate the properties of classes of maximally monotone operators that are uniformly monotone on bounded sets, or uniformly monotone at each point. In particular, we explore connections with various classes of nonexpansive mappings. These classes of monotone operators arise as natural generalizations of subdifferentials of convex functions that are uniformly convex on bounded sets. Some duality results and connections with fixed points are established.</p>

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On Further Notions of Strong Nonexpansiveness and Corresponding Notions of Monotonicity

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Walaa M. Moursi,
  • Jon Vanderwerff

摘要

We investigate the properties of classes of maximally monotone operators that are uniformly monotone on bounded sets, or uniformly monotone at each point. In particular, we explore connections with various classes of nonexpansive mappings. These classes of monotone operators arise as natural generalizations of subdifferentials of convex functions that are uniformly convex on bounded sets. Some duality results and connections with fixed points are established.