IJPAM: Volume 71, No. 3 (2011)

APPROXIMATION-SOLVABILITY OF A SYSTEM OF
GENERALIZED VARIATIONAL INEQUALITIES
IN BANACH SPACES

Tao Cai$^1$, Li Wang$^2$, Min-Hyung Cho$^3$, Shin Min Kang$^4$
$^{1}$Department of Mathematics
Kunming University
Kunming, Yunnan, 650214, P.R. CHINA
$^{2}$Department of Science
Shenyang Institute of Aeronautical Engineering
Shenyang, Liaoning, 110034, P.R. CHINA
$^{3}$Department of Applied Mathematics
Kumoh National Institute of Technology
Gumi, 730-701, KOREA
$^{4}$Department of Mathematics and RINS
Gyeongsang National University
Jinju, 660-701, KOREA


Abstract. In this paper we introduce a new system of generalized variational inequalities and two concepts of $\eta$-subdifferential and $A$-$\eta$-proximal mappings of a proper functional in Banach spaces and prove the existence and Lipschitz continuity of $A$-$\eta$-proximal mapping of a lower semicontinuous $\eta$-subdifferentiable proper functional in reflexive Banach spaces. We suggest a new iterative algorithm for computing the approximate solutions of the system of generalized variational inequalities. Under certain conditions, we establish the existence theorems of solutions and convergence of the iterative algorithm for the system of generalized variational inequalities.

Received: June 2, 2011

AMS Subject Classification: 47J20, 49J40

Key Words and Phrases: $A$-$\eta$-proximal mapping, system of generalized variational inequalities, Banach space

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 3