A general iterative algorithm for monotone operators with lambda-hybrid mappings in Hilbert spaces

作者：Hong Chung Chien^*

来源：Journal of Inequalities and Applications, 2014, 2014(1): 264.

DOI：10.1186/1029-242X-2014-264

• fixed point
• maximal monotone operator
• inverse-strongly monotone mapping
• resolvent
• equilibrium problem
• variational inequality

Let C be a nonempty closed convex subset of a Hilbert space H, let B, G be two set-valued maximal monotone operators on C into H, and let g : H -> H be a k-contraction with 0 < k < 1. A : C -> H is an alpha-inverse strongly monotone mapping, V : H -> H is a (gamma) over bar -strongly monotone and L-Lipschitzian mapping with (gamma) over bar > 0 and L > 0, T : C -> C is a lambda-hybrid mapping. In this paper, a general iterative scheme for approximating a point of F(T) boolean AND (A + B)(-1) 0 boolean AND G(-1) 0 not equal empty set is introduced, where F(T) is the set of fixed points of T, and a strong convergence theorem of the sequence generated by the iterative scheme is proved under suitable conditions. As applications of our strong convergence theorem, the related equilibrium and variational problems are also studied.

• 出版日期2014-7-22