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

Research paper by Chung-Chien Hong

Indexed on: 22 Jul '14Published on: 22 Jul '14Published in: Journal of Inequalities and Applications



Abstract

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 α-inverse strongly monotone mapping, V:H→H is a γ¯-strongly monotone and L-Lipschitzian mapping with γ¯>0 and L>0, T:C→C is a λ-hybrid mapping. In this paper, a general iterative scheme for approximating a point of F(T)∩(A+B)−10∩G−10≠∅ 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.MSC:47H05, 47H10, 58E35.