Derivatives of Set-Valued Maps and Gap Functions for Vector Equilibrium Problems |
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| Authors: | Hadi Mirzaee Majid Soleimani-damaneh |
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| Affiliation: | 1. Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618, Tehran, Iran
2. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran & School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395- 5746, Tehran, Iran
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| Abstract: | This paper deals with the set-valued gap functions for vector equilibrium problems and investigates their differential properties using Hadamard directional differentials. Also, contingent and adjacent derivatives of a class of set-valued maps are characterized. Moreover, some basic properties of Φ-contingent and Φ-adjacent cones are given in the presence of a nonsmooth kernel function. |
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