IJPAM: Volume 50, No. 1 (2009)

ON NONLINEAR MIXED
QUASIVARIATIONAL INEQUALITIES

Haiyan Gao$^1$, Xiu Wan$^2$, Shin Min Kang$^3$, Chahn Yong Jung$^4$
$^1$Kingbridge Business College
Dongbei University of Finance and Economics
Dalian, Liaoning, 116600, P.R. CHINA
e-mail: [email protected]
$^2$Department of Mathematics
Liaoning Normal University
P.O. Box 200, Dalian, Liaoning, 116029, P.R. CHINA
e-mail: [email protected]
$^3$Department of Mathematics
RINS - Research Institute of Natural Sciences
Gyeongsang National University
Jinju, 660-701, KOREA
e-mail: [email protected]
$^4$Department of Business Administration
Gyeongsang National University
Jinju, 660-701, KOREA
e-mail: [email protected]


Abstract.In this paper, we introduce and study a new class of nonlinear mixed quasivariational inequalities in Hilbert spaces. By applying the projection technique, we prove an existence and uniqueness theorem of solution for the nonlinear mixed quasivariational inequality, suggest and analyze an iterative method to compute the approximate solutions of the nonlinear mixed quasivariational inequality and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend and unify some known results in this area.

Received: September 10, 2008

AMS Subject Classification: 47J20, 49J40

Key Words and Phrases: nonlinear mixed quasivariational inequality, projection method, relaxed monotone mapping, strongly monotone mapping, convergence, iterative algorithm

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 1