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Derivatives of Set-Valued Maps and Gap Functions for Vector Equilibrium Problems

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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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Authors and Affiliations

  1. Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618, Tehran, Iran

    Hadi Mirzaee

  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

    Majid Soleimani-damaneh

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  1. Hadi Mirzaee
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  2. Majid Soleimani-damaneh
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Correspondence to Majid Soleimani-damaneh.

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Mirzaee, H., Soleimani-damaneh, M. Derivatives of Set-Valued Maps and Gap Functions for Vector Equilibrium Problems. Set-Valued Var. Anal 22, 673–689 (2014). https://doi.org/10.1007/s11228-014-0286-3

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  • DOI: https://doi.org/10.1007/s11228-014-0286-3

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