Abstract: The notion of “exceptional family of elements (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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