On Further Notions of Strong Nonexpansiveness and Corresponding Notions of Monotonicity

Walaa M. Moursi () and Jon Vanderwerff ()
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Walaa M. Moursi: University of Waterloo
Jon Vanderwerff: La Sierra University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 3, No 9, 24 pages

Abstract: Abstract 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.

Keywords: Convex function; Coercive operator; Nonexpansive mapping; Reflection operator; Uniformly monotone operator; Primary 65K10; 90C25; Secondary 49M29 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02633-4

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