Solvability of implicit complementarity problems

  • Authors:

  • Yeol Je Cho;Jun Li;Nan-Jing Huang

  • Affiliations:

  • Department of Mathematics Education, Research Institute of Natural Sciences, College of Education, Gyeongsang National University, Chinju 660-701, Republic of Korea;School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, PR China and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2007

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Abstract

In this paper, we introduce some new notions of (@a,@c)-exceptional family of elements (in short, (@a,@c)-(EFE)) and (@a,@b,@c)-exceptional family of elements (in short, (@a,@b,@c)-(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, J. Optim. Theory Appl. 104 (2000) 577-588].