@article{Al-Tane2026, 
author = {Ali Al-Tane and See Keong Lee and Messaoud Bounkhel},
title = {On generalized    f-projection and generalized    f-prox-regularity on Banach spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {1},
pages = {661-683},
keywords = {generalized f-projection, V-proximal subdifferential, generalized f-proximal normal cone, uniformly f-prox-regular sets, limiting V-proximal subdifferential, uniformly smooth Banach space, uniformly convex Banach space},
url = {https://www.sciopen.com/article/10.3934/math.2026029},
doi = {10.3934/math.2026029},
abstract = {This paper investigates the connection between the generalized projection        π    S   and the generalized    f-projection        π    S    f  . By introducing an    f-proximal normal cone, defined via the generalized    f-projection, we derive key properties of this set, generalizing established results on the classical    V-proximal normal cone to Banach spaces. Additionally, we propose and examine a new regularity condition called uniform    f-prox-regularity, which extends the standard notion of prox-regularity by leveraging the adaptability of    f-projections.}
}