Bulletin of the Australian Mathematical Society

Research Article

The generalised f-projection operator with an application

Ke-Qing Wua1 and Nan-Jing Huanga1

a1 Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, Peoples Republic of China e-mail: nanjinghuang@hotmail.com

In this paper, we introduce a new concept of generalised f-projection operator which extends the generalised projection operator πK : B*K, where B is a reflexive Banach space with dual space B* and K is a nonempty, closed and convex subset of B. Some properties of the generalised f-projection operator are given. As an application, we study the existence of solution for a class of variational inequalities in Banach spaces.

(Received January 09 2005)