Forward–backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators

  • Vahid Dadashi
  • Mihai PostolacheEmail author
Open Access


In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an \(\alpha \)-inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorithm and prove that the generated sequence converges strongly to a common element of a fixed points set of a nonexpansive mapping and zero points set of the sum of monotone operators. We apply our main result both to equilibrium problems and convex programming.

Mathematics Subject Classification

47H05 47H09 



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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, Sari BranchIslamic Azad UniversitySariIran
  2. 2.China Medical UniversityTaichungTaiwan
  3. 3.Institute of Mathematical Statistics and Applied MathematicsRomanian AcademyBucharestRomania
  4. 4.Department of Mathematics and Computer ScienceUniversity Politehnica of BucharestBucharestRomania

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