Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ON STRONG CONVERGENCE THEOREMS FOR A VISCOSITY-TYPE TSENG'S EXTRAGRADIENT METHODS SOLVING QUASIMONOTONE VARIATIONAL INEQUALITIES

  • Wairojjana, Nopparat (Applied Mathematics Program, Faculty of Science and Technology Valaya Alongkorn Rajabhat University) ;
  • Pholasa, Nattawut (School of Science, University of Phayao) ;
  • Pakkaranang, Nuttapol (Mathematics and Computing Science Program, Faculty of Science and Technology Phetchabun Rajabhat University)
  • Received : 2021.12.01
  • Accepted : 2022.03.14
  • Published : 2022.06.08
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Abstract

The main goal of this research is to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.

Keywords

Acknowledgement

Nattawut Pholasa would like to thank University of Phayao and Thailand Science Research and Innovation grant no. FF65-RIM072 and FF65-UoE001. Nuttapol Pakkaranang would like to thank Phetchabun Rajabhat University.

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