@article{Bounkhel2026, 
author = {Messaoud Bounkhel},
title = {Local    V-Moreau envelope of nonconvex functions},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {21012-21035},
keywords = {local V-Moreau envelope, generalized (f, λ)-projection, p-uniformly convex Banach spaces, q-uniformly smooth Banach spaces, V-primal lower nice functions},
url = {https://www.sciopen.com/article/10.3934/math.2026853},
doi = {10.3934/math.2026853},
abstract = {Recently, the author in 2024 studied the    V-Moreau envelope        e          λ      ,      S        V    f of nonconvex functions    f with index    λ  >  0 and associated with closed sets    S in smooth Banach spaces. In this paper, we developed a corresponding local theory for the local    V-Moreau envelope of    f on a neighborhood of a point              x      ¯       in the domain of    f. A local concept of generalized projection is introduced in connection with the local    V-Moreau envelope. We investigated the Lipschitz continuity, Fréchet differentiability, and    V-proximal subdifferentiability of the local    V-Moreau envelope of    f. Moreover, we established the local Hölder continuity of the local generalized projection for the class of    V-primal lower nice functions introduced and studied in 2020 by Bounkhel et al. Our results extended several known theorems from Hilbert spaces to a more general framework of smooth Banach spaces.}
}