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Implicit and explicit iterative schemes for variational inequalities and fixed point problems of a countable family of strict pseudo-contractions

Journal Name:

  • Mathematica Æterna

Publication Year:

  • 2011

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Let H be a Hilbert space and let {Ti}∞ i=1 be a countable family of strict pseudo-contractions of H into itself such that C = ∩∞ i=1F(Ti) 6= ∅. Assume that F is a nonlinear operator which is -Lipschitzian and - strong monotone on C. In this paper, we devise an implicit and an explicit iterative schemes {xn} from an arbitrary initial point x0 ∈ H for the countable family of mappings {Ti}∞ i=1 and prove that {xn} converges strongly to the solution x∗ of the variational inequality hF(x∗), x − x∗i ≥ 0, ∀x ∈ C.
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