Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators

@inproceedings{Suantai2009StrongCO,
  title={Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators},
  author={Suthep Suantai and Wataru Takahashi},
  year={2009}
}
and Applied Analysis 3 nonexpansive mapping such that F S ∩ A−10/ ∅. Let {xn} be a sequence generated by x0 x ∈ C and un J−1 ( βnJxn ( 1 − βn ) JSJrnxn ) , Cn { z ∈ C : φ z, un ≤ φ z, xn } , Qn {z ∈ C : 〈xn − z, Jx0 − Jxn〉 ≥ 0}, xn 1 ΠCn∩Qnx0 1.6 for all n ∈ N ∪ {0}, where J is the duality mapping on E, {βn} ⊂ 0, 1 , and {rn} ⊂ a,∞ for some a > 0. If lim infn→∞ 1 − βn > 0, then {xn} converges strongly to ΠF S ∩A−10x0, where ΠF S ∩A−10 is the generalized projection of E onto F S ∩A−10. The… CONTINUE READING

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References

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Showing 1-10 of 22 references

Weak and strong convergence theorems for maximal monotone operators in a Banach space,

  • S. Kamimura, F. Kohsaka, W. Takahashi
  • Set-Valued Analysis,
  • 2004

Weak convergence of orbits of nonlinear operators in reflexive Banach spaces

  • S. Reich D. Butnariu, A. J. Zaslavski
  • Numerical Functional Analysis and Optimization
  • 2003

Asymptotic behavior of relatively nonexpansive operators in Banach spaces

  • S. Reich D. Butnariu, A. J. Zaslavski
  • Journal of Applied Analysis
  • 2001

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