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MATEMATIČKI VESNIK
An iterative method for variational inequality problems and fixed point problems in Hilbert spaces
Xiaolong Qin, Meijuan Shang and Yongfu Su

Abstract

In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a relaxed $(\gamma,r)$-cocoercive, Lipschitz continuous mapping. Our results improve and extend the corresponding results of many others.

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Keywords: Projection method; relaxed cocoercive mapping; nonexpansive mapping; fixed point.

MSC: 47H05, 47H09; 47J05; 47J25

Pages:  107$-$120     

Volume  60 ,  Issue  2 ,  2008