Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
نویسندگان
چکیده
Let B be a real Banach space with the dual space B∗. Let φ : B → R ∪ { ∞} be a proper functional and let Θ : B × B → R be a bifunction. In this paper, a new concept of η-proximal mapping of φ with respect to Θ is introduced. The existence and Lipschitz continuity of the η-proximal mapping of φ with respect to Θ are proved. By using properties of the η-proximal mapping of φ with respect to Θ, a generalized mixed equilibrium problem with perturbation for short, GMEPP is introduced and studied in Banach space B. An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space B, and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in B H a Hilbert space.
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