Journal of Zhejiang University-SCIENCE A

, Volume 6, Issue 4, pp 289–295 | Cite as

Exceptional family of elements and the solvability of complementarity problems in uniformly smooth and uniformly convex Banach spaces

Applied Mathematics and Engineering Management Science


The notion of “exceptional family of elments (EFE)” plays a very important role in solving complementarity problems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.

Key words

Exceptional family of elements (EFE) Banach spaces and complementarity 

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© Zhejiang University Press 2005

Authors and Affiliations

  1. 1.Department of MathematicsRoyal Military College of CanadaKingstonCanada
  2. 2.Department of MathematicsShawnee State UniversityPortsmouthUSA

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