Auxiliary principle and iterative algorithm for a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities

In this paper, the auxiliary principle technique is extended to study a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities problem in Hilbert spaces. First, we establish the existence of solutions of the corresponding system of auxiliary variationa...

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Bibliographic Details
Published in:Journal of inequalities and applications 2016-02, Vol.2016 (1), p.1-14, Article 38
Main Authors: Qiu, Yang-Qing, Chen, Jin-Zuo, Ceng, Lu-Chuan
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
auxiliary principle
Construction
Convergence
Inequalities
iterative algorithm
Iterative algorithms
Iterative methods
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinearity
system of generalized mixed implicit quasi-variational-like inequalities
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Summary:In this paper, the auxiliary principle technique is extended to study a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities problem in Hilbert spaces. First, we establish the existence of solutions of the corresponding system of auxiliary variational inequalities problem. Then, using the existence result, we construct a new iterative algorithm. Finally, both the existence of solutions of the original problem and the convergence of iterative sequences generated by the algorithm are proved. We give an affirmative answer to the open problem raised by Noor et al. (Korean J. Comput. Appl. Math. 1:73-89, 1998 ; J. Comput. Appl. Math. 47:285-312, 1993 ). Our results improve and extend some known results.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-016-0978-3