Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces

نویسندگان

  • Dan Zhang
  • Xiaolong Qin
  • Feng Gu
چکیده

Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S {T s : 0 ≤ s < ∞} with a common fixed point, a contraction f with the coefficient 0 < α < 1, and a strongly positive linear bounded self-adjoint operator A with the coefficient γ > 0. Let 0 < γ < γ/α. It is proved that the sequence {xn} generated by the iterative method x0 ∈ H, xn 1 αnγf xn βnxn 1 − βn I − αnA 1/sn ∫sn 0 T s xnds, n ≥ 0 converges strongly to a common fixed point x∗ ∈ F S , where F S denotes the common fixed point of the nonexpansive semigroup. The point x∗ solves the variational inequality 〈 γf −A x∗, x − x∗〉 ≤ 0 for all x ∈ F S .

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عنوان ژورنال:
  • J. Applied Mathematics

دوره 2012  شماره 

صفحات  -

تاریخ انتشار 2012