Abstract
We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.
Highlights
Throughout this paper, we assume that H is a real Hilbert space with inner product ⟨⋅, ⋅⟩ and norm ‖ ⋅ ‖, C is a nonempty closed convex subset of H, and PC is the metric projection of H onto C
Motivated and inspired by the above facts, in this paper, we introduce and analyze a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inclusion (11) in a real Hilbert space
We will prove a strong convergence theorem for a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inclusion (11) in a real Hilbert space
Summary
Throughout this paper, we assume that H is a real Hilbert space with inner product ⟨⋅, ⋅⟩ and norm ‖ ⋅ ‖, C is a nonempty closed convex subset of H, and PC is the metric projection of H onto C. Note that the nonexpansivity of Si implies the nonexpansivity of Wn. In 2008, Colao et al [37] introduced and studied an iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space H. Motivated and inspired by the above facts, in this paper, we introduce and analyze a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inclusion (11) in a real Hilbert space. The results obtained in this paper improve and extend the corresponding results announced by many others
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
