Relaxed and hybrid viscosity methods for general system of variational inequalities with split feasibility problem constraint

• Published in: Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2013; no. 1; p. 43
• Main Authors: Ceng, Lu-Chuan, Yao, Jen-Chih
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 27.02.2013; BioMed Central Ltd
• Subjects: Analysis; Applications of Mathematics; Differential Geometry; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Proceedings of the International Congress in Honour of Professor Hari M. Srivastava; Topology; general system of variational inequalities; split feasibility problem; relaxed and hybrid viscosity methods; fixed point problem; strong convergence
• ISSN: 1687-1812; 1687-1812
• DOI: 10.1186/1687-1812-2013-43

In this paper, we propose and analyze some relaxed and hybrid viscosity iterative algorithms for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem and the fixed point set Fix ( S ) of a strictly pseudocontractive mapping S in the setting of infinite-dimensional Hilbert spaces. We prove that the sequences generated by the proposed algorithms converge strongly to an element of Fix ( S ) ∩ Ξ ∩ Γ under mild conditions. AMS Subject Classification: 49J40, 47H05, 47H19.