On generalized $ f $-projection and generalized $ f $-prox-regularity on Banach spaces
Abstract
This paper investigates the connection between the generalized projection $ \pi_S $ and the generalized $ f $-projection $ \pi_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.
Fields of Study & Subjects
Optimization and Variational Analysis
Advanced Banach Space Theory
Fixed Point Theorems Analysis
Publication details
- Journal / source
- AIMS Mathematics
- Volume
- 11
- Issue
- 1
- Pages
- 661–683
- Publication date
- 1 January 2026