An explicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of an infinite family of nonexpansive mappings

摘要: Abstract Let H be a Hilbert space and C nonempty closed convex subset of , { T i } ∈ N family nonexpansive mappings from into G : × → R finite equilibrium functions ( 1 2 … K ) A strongly positive bounded linear operator with coefficient γ B λ -Lipschitzian, relaxed μ ν -cocoercive map . Moreover, let r k n = α satisfy appropriate conditions F ≔ ∩ E P V I x ≠ 0 ; we introduce an explicit scheme which defines suitable sequence as follows: + f − W s S ⋯ ∀ converges to ∗ satisfies the variational inequality 〈 〉 ≥ for all The results presented in this paper mainly extend improve recent result Colao [V. Colao, An implicit method finding common solutions inequalities systems problems fixed points infinite mappings, Nonlinear Analysis (2009), doi:10.1016/j.na.2009.01.115 ] Qin [X. Qin, M. Shang, Y. Su, general iterative point spaces, 69 (2008) 3897–3909].