In this paper, we continue the study of the -prox-regularity that we have started recently for sets. We define an appropriate concept of the -prox-regularity for functions in reflexive smooth Banach spaces by adapting the one given in Hilbert spaces. Our main goal is to study the relationship between the -prox-regularity of a given l.s.c. and the -prox-regularity of its epigraph.

中文翻译：

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光滑Banach空间中的-Prox-Regular函数

在本文中，我们继续的研究- PROX规律性，我们最近开始为套。我们定义的适当概念-通过适应Hilbert空间中给出的PROX规律性的自反光滑Banach空间的功能。我们的主要目标是研究之间的关系-一个给定的LSC的PROX规律性和-其题词的PROX规律性。