Iterative common solutions for monotone inclusion problems, fixed point problems and equilibrium problems
Wataru Takahashi, Ngai‐Ching Wong, Jen‐Chih Yao · Fixed Point Theory and Applications · 2012
Abstract Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Let α > 0 , and let A be an α-inverse strongly-monotone mapping of C into H. Let T be a generalized hybrid mapping of C into H. Let B and W be maximal monotone operators on H such that the domains of B and W are included in C. Let 0 0 and L > 0 . Take μ , γ ∈ R as follows: 0 < μ < 2 γ ¯ L 2 , 0 < γ < γ ¯ − L 2 μ 2 k . Suppose that F ( T ) ∩ ( A + B ) − 1 0 ∩ W − 1 0 ≠ ∅ , where F ( T ) and ( A + B ) − 1 0 , W − 1 0 are the set of fixed points of T and the sets of zero points of A + B and W, respectively. In this paper, we prove a strong convergence theorem for finding a point z 0 of F ( T ) ∩ ( A + B ) − 1 0 ∩ W − 1 0 , where z 0 is a unique fixed point of P F ( T ) ∩ ( A +