Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Hybrid Algorithms for Ky Fan Inequalities and Common Fixed Points of Demicontractive Single-valued and Quasi-nonexpansive Multi-valued Mappings

  • Onjai-uea, Nawitcha (Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University) ;
  • Phuengrattana, Withun (Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University)
  • Received : 2017.12.30
  • Accepted : 2018.12.06
  • Published : 2019.12.23
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Abstract

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

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References

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