J. Korean Math. Soc. 2008; 45(1): 163-176
Printed January 1, 2008
Copyright © The Korean Mathematical Society.
Lili Zhang, Zeqing Liu, and Shin Min Kang
Dalian University of Technology, Liaoning Normal University, Gyeongsang National University
In this paper, we introduce and study a new class of generalized nonlinear variational-like inequalities. By employing the auxiliary principle technique we suggest an iterative algorithm to compute approximate solutions of the generalized nonlinear variational-like inequalities. We discuss the convergence of the iterative sequences generated by the algorithm in Banach spaces and prove the existence of solutions and convergence of the algorithm for the generalized nonlinear variational-like inequalities in Hilbert spaces, respectively. Our results extend, improve and unify several known results due to Ding, Liu et al, and Zeng, and others.
Keywords: generalized nonlinear variational-like inequality, auxiliary principle technique, fixed points, algorithms, reflexive Banach space, Hilbert space
MSC numbers: 47J20, 49J40
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