Three-step iterative algorithms for solving the system of generalized mixed quasi-variational-like inclusions

Authors:
Lu-Chuan Zeng;Sy-Ming Guu;Jen-Chih Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Department of Business Administration, College of Management, Yuan-Ze University, Chung-Li City, Taoyuan Hsien, Taiwan 330, ROC;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804, ROC
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

In this paper, we consider the system of generalized mixed quasi-variational-like inclusions in Hilbert spaces. We extend the auxiliary principle technique to develop a three-step iterative algorithm for solving the system of generalized mixed quasi-variational-like inclusions. Under the assumptions of the continuity and partially relaxed @h-strong monotonicity of set-valued mappings, we establish the convergence for our algorithm. Our algorithm and its convergence results are new, and generalize Ding's predictor-corrector iterative algorithms. Moreover, our results unify some known results in the literature as well.