Systems of variational inequalities with hierarchical variational inequality constraints for Lipschitzian pseudocontractions


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	Systems of variational inequalities with hierarchical variational inequality constraints for Lipschitzian pseudocontractions


	Fixed Point Theory, Volume 20, No. 1, 2019, 113-134, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.07 Authors: Lu-Chuan Ceng, Adrian Petruşel, Jen-Chih Yao and Yonghong Yao Abstract: In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an accretive operator in a real Banach space. We propose an implicit composite extragradient-like method based on the Mann iteration method, the viscosity approximation method and the Korpelevich extragradient method. Convergence results for the proposed iteration method are also established under some suitable assumptions. Key Words and Phrases: Implicit composite extragradient-like method, general system of variational inequalities, fixed point, accretive operator, uniform convexity, uniform smoothness. 2010 Mathematics Subject Classification: 49J30, 47H09, 47H10, 47J20. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents