Lili Zhang, Zeqing Liu, Jong Seo Park, Shin Min Kang
Basic Courses Teaching Department
Dalian Neusoft Institute of Information
Dalian, Liaoning, 116023, P.R. CHINA
Department of Mathematics
Liaoning Normal University
Dalian, Liaoning, 116029, P.R. CHINA
Departemnt of Mathematics Education
Chinju National University of Education
Jinju, 660-756, KOREA
Department of Mathematics and RINS
Gyeongsang National University
Jinju, 660-701, KOREA

Abstract. In this paper, a new class of variational inequalities, which are called the generalized nonlinear variational-like inequalities are introduced and analyzed in Hilbert spaces. Making use of the auxiliary principle technique, some existence theorems of solutions for the generalized nonlinear variational-like inequalities are proved and an iterative algorithm to compute the approximate solutions is constructed. Some stability results of iterative sequences generated by the iterative algorithm are also discussed. These results presented here are the extensions and improvements of the earlier and recent results in this field.

Received: June 8, 2011

AMS Subject Classification: 47J20, 49J40

Key Words and Phrases: generalized nonlinear variational-like inequality, auxiliary principle technique, iterative algorithm, stability

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