Glasnik Matematicki, Vol. 46, No.1 (2011), 233-247.

APPROXIMATING COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES BY ITERATIVE ALGORITHMS WITH APPLICATIONS

Xiaolong Qin, Sun Young Cho and Yeol Je Cho

Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
e-mail: ooly61@yahoo.co.kr

Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Korea
e-mail: yjcho@gnu.ac.kr

Abstract.   In this paper, we introduce an iterative scheme for a general variational inequality. Strong convergence theorems of common solutions of two variational inequalities are established in a uniformly convex and 2-uniformly smooth Banach space. As applications, we, still in Banach spaces, consider the convex feasibility problem.

2000 Mathematics Subject Classification.   47H05, 47H09, 47J25.

Key words and phrases.   Iterative algorithm, variational inequality, inverse-strongly accretive mapping, sunny nonexpansive retraction.

DOI: 10.3336/gm.46.1.17

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