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Solvability of implicit complementarity problems

โœ Scribed by Yeol Je Cho; Jun Li; Nan-jing Huang

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
233 KB
Volume
45
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

In this paper, we introduce some new notions of (ฮฑ, ฮณ )-exceptional family of elements (in short, (ฮฑ, ฮณ )-(EFE)) and (ฮฑ, ฮฒ, ฮณ )-exceptional family of elements (in short, (ฮฑ, ฮฒ, ฮณ )-(EFE)) for a pair of continuous functions involved in the implicit complementarity problem (in short, ICP). Based upon these notions and the topological degree theory, we studied the feasibility and strictly feasibility of (ICP) in R n and an infinite-dimensional Hilbert space H , respectively. As special cases, we obtain the feasibility and strictly feasibility of complementarity problems and partly answered the second open problem (P2) proposed by Isac [G. Isac, Exceptional families of elements, feasibility and complementarity,

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