RELAXED PROJECTION-VISCOSITY APPROXIMATION METHOD

• Published in: Taiwanese journal of mathematics Vol. 16; no. 3; pp. 1105 - 1124
• Main Authors: Ceng, L. C., Petruşel, A., Wong, M. M.
• Format: Journal Article
• Language: English
• Published: Mathematical Society of the Republic of China 01.06.2012
• Subjects: Approximation; Hilbert spaces; Inner products; Iterative methods; Mathematical monotonicity; Mathematical sets; Real numbers; Variational inequalities
• ISSN: 1027-5487; 2224-6851; 2224-6851
• DOI: 10.11650/twjm/1500406681

The purpose of this paper is to investigate the problem of finding a common element of the solution set of a general system of variational inequalities, the solution set of a variational inequality problem and the fixed point set of a strict pseudocontraction in a real Hilbert space. Based on the well-known viscosity approximation method, extragradient method and Mann's iteration method, we propose and analyze a relaxed projection-viscosity approximation method for computing a common element. Under very mild assumptions, we obtain a strong convergence theorem for three sequences generated by the proposed method. Our proposed method is quite general and flexible and develops some iterative methods considered in the earlier and recent literature. 2010Mathematics Subject Classification: 49J40, 65K05, 47H09. Key words and phrases: General system of variational inequalities, Strict pseudocontraction, Inverse-strongly monotone mapping, Relaxed projection-viscosity approximation method, Strong convergence.