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  • Bulletin of the Australian Mathematical Society, Volume 73, Issue 2
  • April 2006, pp. 307-317

The generalised f-projection operator with an application

  • Ke-Qing Wu (a1) and Nan-Jing Huang (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700038892
  • Published online: 01 April 2009
Abstract

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.

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[4]Y. Alber , R. Burachik and A. Iusem , ‘A proximal point method for nonsmooth convex optimization problems in Banach spaces’, Abstr. Appl. Anal. 2 (1997), 97120.

[5]Y. Alber and S. Guerre-Delabriere , ‘On the projection methods for fixed point problem’, Analysis 21 (2001), 730.

[6]Y. Alber and A. Iusem , ‘Extension of subgradient techniques for nonsmooth optimization in Banach spaces’, Set-Valued Anal. 9 (2001), 315335.

[7]Y. Alber , ‘Proximal projection method for variational inequalities and Cesáro averaged approximations’, Comput. Math. Appl. 43 (2002), 11071124.

[9]Y. Alber and M. Nashed , ‘Iterative-projection regularization of unstable variational inequalities’, Analysis 24 (2004), 1939.

[11]K. Fan , ‘A generalization of Tychonoff's fixed point theorem’, Math. Ann. 142 (1961), 305310.

[12]F. Giannessi and A. Maugeri , Variational inequalities and network equilibrium problems (Plenum, New York, 1995).

[15]W.K. Kirk and B. Sims , Handbook of metric fixed point theory (Kluwer Academic Publishers, Dordrecht, 2001).

[16]J. Li , ‘On the existence of solutions of variational inequalities in Banach spaces’, J. Math. Anal. Appl. 295 (2004), 115126.

[17]J. Li , ‘The generalized projection operator on reflexive Banach spaces and its applications’, J. Math. Anal. Appl. 306 (2005), 5571.

[20]G.X.Z. Yuan , KKM theory and applications in nonlinear analysis (Marcel-Dekker, New York, 1999).

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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