2015
DOI: 10.1080/00036811.2015.1051971
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Hybrid viscosity methods for equilibrium problems, variational inequalities, and fixed point problems

Abstract: In this paper, we introduce a hybrid viscosity iterative algorithm for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of general system of variational inequalities, the set of common fixed points of one finite family of nonexpansive mappings, and another infinite family of nonexpansive mappings in a real Hilbert space. This hybrid viscosity iterative algorithm is based on viscosity approximation method, Mann's iterative method, projection method, s… Show more

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Cited by 12 publications
(8 citation statements)
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“…Let T i : C → C be a nonexpansive mapping for each i = 1, 2, ... such that F := ∞ i=1 Fix(T i ) ∩ GSVI(C, A, B) ∅, and f ∈ Ω with contractive constant ∈ (0, 1). Let {V k } ∞ k=1 be defined by (7) and (8).…”
Section: Resultsmentioning
confidence: 99%
See 3 more Smart Citations
“…Let T i : C → C be a nonexpansive mapping for each i = 1, 2, ... such that F := ∞ i=1 Fix(T i ) ∩ GSVI(C, A, B) ∅, and f ∈ Ω with contractive constant ∈ (0, 1). Let {V k } ∞ k=1 be defined by (7) and (8).…”
Section: Resultsmentioning
confidence: 99%
“…Let T i : C → C be a nonexpansive mapping for each i = 1, 2, ... such that F := ∞ i=1 Fix(T i ) ∩ GSVI(C, A, B) ∅, and f ∈ Ω with contractive constant ∈ (0, 1). Let {V k } ∞ k=1 be defined by (7) and (8). Given sequences {ι k } ∞ k=1 , {τ k } ∞ k=1 in [0, 1] and { k } ∞ k=1 in (0, 1], the following conditions are satisfied: (C1) 0 < τ k ≤ 1 − , ∀k ≥ k 0 for some k 0 ≥ 1, and…”
Section: Resultsmentioning
confidence: 99%
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“…In 2014, Bnouhachem [2] proposed a modified projection method for computing a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in Hilbert space, and proved the strong convergence of the iteration sequences. Since the iterative algorithms played an important role for solving integral and differential equations, optimization problems, image reconstruction problems, game theory and other fields such as [5,16,19,20,22], the convergence and construction of the iteration algorithm for computing fixed points has attracted more and more attentions see, e.g., [3,6,12,18,21].…”
Section: Introductionmentioning
confidence: 99%