Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weak and Strong Convergence of Hybrid Subgradient Method for Pseudomonotone Equilibrium Problems and Nonspreading-Type Mappings in Hilbert Spaces

  • Sriprad, Wanna (Department of Mathematics and Computer Scicence, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi) ;
  • Srisawat, Somnuk (Department of Mathematics and Computer Scicence, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi)
  • Received : 2016.10.16
  • Accepted : 2019.01.28
  • Published : 2019.03.23
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Abstract

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of ${\kappa}$-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

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References

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