On -subdifferentiable and [{\mit\Phi}+\gamma]-subdifferentiable Functions
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 273-279
MSC: 46N10, 26E15, 52A01.
DOI: 10.4064/ba53-3-4
Abstract
Let X be an arbitrary set. Let {\mit\Phi} be a family of real-valued functions defined on X. Let \gamma:X\times X\to \mathbb R. Set [{\mit\Phi}+\gamma]=\{ \phi(\cdot)+ \gamma(\cdot,x)\mid \phi \in {\mit\Phi},\, x \in X\}. We give conditions guaranteeing the equivalence of {\mit\Phi}^{\gamma(\cdot,\cdot)}-subdifferentiability and [{\mit\Phi}+\gamma]-subdifferentiability.
