Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2008; 45(1): 163-176

Printed January 1, 2008

Copyright © The Korean Mathematical Society.

On solvability of generalized nonlinear variational-like inequalities

Lili Zhang, Zeqing Liu, and Shin Min Kang

Dalian University of Technology, Liaoning Normal University, Gyeongsang National University

Abstract

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