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The generalised f-projection operator with an application

Published online by Cambridge University Press:  17 April 2009

Ke-Qing Wu  and
Nan-Jing Huang
Ke-Qing Wu
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, Peoples Republic of China e-mail: nanjinghuang@hotmail.com
Nan-Jing Huang
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, Peoples Republic of China e-mail: nanjinghuang@hotmail.com
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 307 - 317
Copyright
Copyright © Australian Mathematical Society 2006

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