Relaxed Quasimonotone Operators and Relaxed Quasiconvex Functions

M. R. Bai and N. Hadjisavvas ()
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M. R. Bai: Hunan University
N. Hadjisavvas: University of the Aegean

Journal of Optimization Theory and Applications, 2008, vol. 138, issue 3, No 1, 329-339

Abstract: Abstract In this paper, we introduce the class of multivalued relaxed μ quasimonotone operators and establish the existence of solutions of variational inequalities for such operators. This result is compared with a recent result of Bai et al. on densely relaxed pseudomonotone operators. A similar comparison regarding an existence result of Luc on densely pseudomonotone operators is provided. Also, we introduce a broad class of functions, called relaxed quasiconvex functions, and show that they are characterized by the relaxed μ quasimonotonicity of their subdifferentials. The results strengthen a variety of other results in the literature.

Keywords: Variational inequalities; Relaxed μ quasimonotone operators; Relaxed quasiconvex functions; Subdifferentials; Dag subdifferential (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-008-9382-6

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