Subdifferential characterization ofs-lower regular functions

Moreau envelopes of s-lower regular functions

“…Our aim in this paper consists in extending in some sense the study of the Moreau envelope and its proximal mapping to another important new class of functions, namely the s-lower regular functions, continuing in this way our work [19]. We generalize the results obtained in [28,4,23,24] in more general spaces as uniformly convex and uniformly smooth Banach spaces, in view of further applications to evolution problems in L p -spaces.…”

“…We recall now the concept of s-lower regular functions that we developed in [19]. The class of such functions is an adaptation of the class of primal lower nice functions introduced in [27] and of similar classes in [11]; see also [2,5,6,[15][16][17]21,24,31].…”

“…One of the fundamental other examples of s-lower regular functions is provided (see [19]) by convexly C 1,s -composite functions which are qualified. One of the fundamental other examples of s-lower regular functions is provided (see [19]) by convexly C 1,s -composite functions which are qualified.…”

“…The following theorem from [19] shows that the definition of s-lower regularity can be given with any of the above subdifferentials. The following theorem from [19] shows that the definition of s-lower regularity can be given with any of the above subdifferentials.…”