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Convergence of Two Splitting Projection Algorithms in Hilbert Spaces

Author

Listed:
  • Marwan A. Kutbi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Abdul Latif

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Xiaolong Qin

    (Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

Abstract

The aim of this present paper is to study zero points of the sum of two maximally monotone mappings and fixed points of a non-expansive mapping. Two splitting projection algorithms are introduced and investigated for treating the zero and fixed point problems. Possible computational errors are taken into account. Two convergence theorems are obtained and applications are also considered in Hilbert spaces

Suggested Citation

  • Marwan A. Kutbi & Abdul Latif & Xiaolong Qin, 2019. "Convergence of Two Splitting Projection Algorithms in Hilbert Spaces," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:922-:d:273227
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    References listed on IDEAS

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    2. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
    3. Jonathan Eckstein & Michael C. Ferris, 1998. "Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 218-235, May.
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