Some relationships among quasidifferential,weak subdifferential and exhausters |
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Authors: | Mahide Küçük Ryszard Urbański Jerzy Grzybowski Yalçın Küçük İlknur Atasever Güvenç |
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Institution: | 1. Faculty of Science, Department of Mathematics, Anadolu University, Eski?ehir, Turkey.;2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland. |
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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. |
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Keywords: | Exhauster quasidifferential weak subdifferential |
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