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ISSN : 1226-0657

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Vol.11 No.2

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Vector Variational Inequality Problems with Generalized $C(x)$-$L$-pseudomonotone Set-valued Mappings

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2004, v.11 no.2, pp.155-166
Lee, Byung-Soo
Kang, Mee-Kwang
Lee,, B. , & Kang,, M. (2004). Vector Variational Inequality Problems with Generalized $C(x)$-$L$-pseudomonotone Set-valued Mappings. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(2), 155-166.

Abstract

In this paper, we introduce new monotone concepts for set-valued mappings, called generalized C(x)-L-pseudomonotonicity and weakly C(x)-L-pseudomonotonicity. And we obtain generalized Minty-type lemma and the existence of solutions to vector variational inequality problems for weakly C(x)-L-pseudomonotone set-valued mappings, which generalizes and extends some results of Konnov & Yao [11], Yu & Yao [20], and others Chen & Yang [6], Lai & Yao [12], Lee, Kim, Lee & Cho [16] and Lin, Yang & Yao [18].

keywords
Generalized C(x)-L-pseudomonotone, weakly C(x)-L-pseudomonotone, Minty-type lemma, variational inequality, KKM-Fan theorem

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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