On generalized ϵ-subdifferential and radial epiderivative of set-valued mappings

In this paper, a generalized $\mathit{ϵ}$ ‐subdifferential, which was defined by the radial epiderivative and a norm, is first introduced for a set‐valued mapping. Some existence theorems of the generalized $\mathit{ϵ}$ ‐subdifferential and the radial epiderivative are discussed. A relationship between the existence of the radial epiderivative and the existence of the generalized $\mathit{ϵ}$ ‐subdifferential is investigated for a set‐valued mapping.