Abstract
In this paper, we introduce and study iterative algorithms for solving split mixed equilibrium problems and fixed point problems of λ-hybrid multivalued mappings in real Hilbert spaces and prove that the proposed iterative algorithm converges weakly to a common solution of the considered problems. We also provide an example to illustrate the convergence behavior of the proposed iteration process.
Highlights
Let H be a real Hilbert space with inner product ·, · and induced norm ·
Motivated and inspired by the above results and related literature, we propose an iterative algorithm for finding a common element of the set of solutions of split mixed equilibrium problems and the set of fixed points of λ-hybrid multivalued mappings in real Hilbert spaces
3 Main results we prove the weak convergence theorems for finding a common element of the set of solutions of split mixed equilibrium problems and the set of fixed points of λ-hybrid multivalued mappings in real Hilbert spaces and give a numerical example to support our main result
Summary
Let H be a real Hilbert space with inner product ·, · and induced norm ·. Let C be a nonempty closed convex subset of H, φ : C → R be a function, and F : C × C → R be a bifunction. The mixed equilibrium problem is to find x ∈ C such that. ). The solution set of mixed equilibrium problem is denoted by MEP(F, φ). If φ = , this problem reduces to the equilibrium problem, which is to find x ∈ C such that F(x, y) ≥ , ∀y ∈ C. The solution set of equilibrium problem is denoted by EP(F). The mixed equilibrium problem is very general in the sense that it includes, as special cases, optimization problems, variational inequality problems, minimization problems, fixed point problems, Nash equilibrium problems in noncooperative games, and others; see, e.g., [ – ]
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