Some relationships among quasidifferential, weak subdifferential and exhausters. (1st November 2016) - Küçük, Mahide; Urbański, Ryszard; Grzybowski, Jerzy; Küçük, Yalçın; Atasever Güvenç, İlknur and Tozkan, Didem and Soyertem, Mustafa
Abstract : In this study, some relationships between quasidifferentiability and weakly subdifferentiability of a function are investigated, and some results on calculating the quasidifferential in terms of weak exhausters are presented. Moreover, under some assumptions weak subdifferentiability of a quasidifferentiable function is proved and the weak subdifferential is obtained by using the quasidifferential. Under some assumptions, it is proved that a positively homogeneous and lower semicontinuous function is quasidifferentiable. It is also shown that directional differentiability and weak subdifferentiability imply quasidifferentiability. Furthermore, a method to evaluate the quasidifferential is given by using reduced weak lower exhausters.