Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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HYBRID INERTIAL CONTRACTION PROJECTION METHODS EXTENDED TO VARIATIONAL INEQUALITY PROBLEMS

  • Truong, N.D. (Department of Mathematics, Hai Phong University) ;
  • Kim, J.K. (Department of Mathematics Education, Kyungnam University) ;
  • Anh, T.H.H. (Department of Mathematics, Hai Phong University)
  • Received : 2021.05.12
  • Accepted : 2021.11.27
  • Published : 2022.03.15
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Abstract

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

Keywords

Acknowledgement

This work was supported by the Basic Science Research Program through the National Research Foundation(NRF) Grant funded by Ministry of Education of the republic of Korea (2018R1D1A1B07045427).

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