Abstract
We introduce a new iterative algorithm for approximating a common element of the set of solutions for mixed equilibrium problems, the set of solutions of a system of quasi-variational inclusion, and the set of fixed points of an infinite family of nonexpansive mappings in a real Hilbert space. Strong convergence of the proposed iterative algorithm is obtained. Our results generalize, extend, and improve the results of Peng and Yao, 2009, Qin et al. 2010 and many authors.
Highlights
Throughout this paper, we assume that H is a real Hilbert space with inner product and norm denoted by ⟨⋅, ⋅⟩ and ‖ ⋅ ‖, respectively
In 2010, Qin et al [22] introduced an iterative method for finding solutions of a generalized equilibrium problem, the set of fixed points of a family of nonexpansive mappings, and the common variational inclusions
We proved the strong convergence theorem under certain appropriate conditions
Summary
Throughout this paper, we assume that H is a real Hilbert space with inner product and norm denoted by ⟨⋅, ⋅⟩ and ‖ ⋅ ‖, respectively.
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