IJPAM: Volume 16, No. 1 (2004)


Zeqing Liu$^1$, Jeong Sheok Ume$^2$, Shin Min Kang$^3$
$^1$Department of Mathematics
Liaoning Normal University
P.O. Box 200, Dalian, Liaoning, 116029, P.R. CHINA
e-mail: zeqingliu@sina.com.cn
$^2$Department of Applied Mathematics
Changwon National University
#9 Sarim-ddong, Changwon, Gyeong-Nam, 641-773, KOREA
e-mail: jsume@changwon.ac.kr
$^3$Department of Mathematics and Research Institute of Natural Science
Gyeongsang National University
Chinju, 660-701, KOREA
e-mail: smkang@nongae.gsnu.ac.kr

Abstract.In this paper, we introduce and study a new class of completely generalized quasivariational inequalities and construct new iterative algorithms by using the projection technique. We establish the existence of solutions for the class of completely generalized quasivariational inequalities involving relaxed Lipschitz mappings, strongly monotone mappings and generalized pseudocontractive mappings. Under suitable conditions, the convergence analyses of the iterative algorithm are also studied. Our results are the extension and improvements of the earlier and recent results in this field.

Received: July 19, 2004

AMS Subject Classification: 47J20, 49J40

Key Words and Phrases: completely generalized quasivariational inequality, projection method, relaxed Lipschitz mapping, strongly monotone mapping, generalized pseudocontractive mapping

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 1