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The purpose of this paper is to introduce a new hybrid extragradient iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and satisfying solutions of the split feasibility problem (SFP) and systems of equilibrium problem (SEP) in Hilbert spaces. We prove that the sequence generated by the proposed(More)
and Applied Analysis 3 PK is called the metric projection ofH ontoK. It is well known that PK is a nonexpansive mapping ofH onto K and satisfies 〈x − y, PKx − PKy〉 ≥ ∥ PKx − PKy ∥ ∥ 2 , 2.3 for every x, y ∈ H. Moreover, PKx is characterized by the following properties: PKx ∈ K and 〈x − PKx, y − PKx〉 ≤ 0, ∥ ∥x − y∥∥ ≥ ‖x − PKx‖ ∥ ∥y − PKx ∥
In this paper, we introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove strong convergence theorems for nonexpansive mapping to solve a unique solution of the variational inequality. The results extended(More)
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