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Volume 3, Issue 2, 31 August 2021, Pages 133-147
Abstract. We introduce the notions of operator-dependent normality and operator-dependent weak normality with respect to a given convex function, which is uniformly continuous on bounded sets, and a given operator. In 2001, Gabour, Reich and Zaslavski considered bounded sets and studied the properties of normal mappings and normal sequences of mappings with respect to an everywhere uniformly continuous convex function. In 2020, Barshad, Reich and Zaslavski studied similar properties for not necessarily bounded sets, and also introduced the more general notion of weak normality. In this paper, we investigate the analogous properties regarding certain developments of these concepts and present some applications to the minimization of convex functions.
How to Cite this Article:
Kay Barshad, Simeon Reich, Alexander Zaslavski, Generic properties of operator-dependent normal mappings, Appl. Set-Valued Anal. Optim. 3 (2021), 133-147.