Abstract
We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).
Highlights
We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space
Let H be a real Hilbert space, whose inner product and norm are denoted by ⟨⋅, ⋅⟩ and ‖⋅‖, respectively
Let {Sn}∞ n=1 : C → C be a family of infinitely nonexpansive mappings, such that ⋂∞ n=1 F(Sn) ≠ 0, and let {λn}∞ n=1 be a sequence of positive numbers in [0, b] for some b ∈ (0, 1)
Summary
Let H be a real Hilbert space, whose inner product and norm are denoted by ⟨⋅, ⋅⟩ and ‖⋅‖, respectively. We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. We will introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the variational inequality problem, and the equilibrium problem.
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