Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ACCELERATED STRONGLY CONVERGENT EXTRAGRADIENT ALGORITHMS TO SOLVE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS IN REAL HILBERT SPACES

  • Nopparat Wairojjana (Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage Pathum Thani Province) ;
  • Nattawut Pholasa (School of Science, University of Phayao) ;
  • Chainarong Khunpanuk (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University) ;
  • Nuttapol Pakkaranang (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University)
  • Received : 2022.12.22
  • Accepted : 2024.04.14
  • Published : 2024.06.15
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Abstract

Two inertial extragradient-type algorithms are introduced for solving convex pseudomonotone variational inequalities with fixed point problems, where the associated mapping for the fixed point is a 𝜌-demicontractive mapping. The algorithm employs variable step sizes that are updated at each iteration, based on certain previous iterates. One notable advantage of these algorithms is their ability to operate without prior knowledge of Lipschitz-type constants and without necessitating any line search procedures. The iterative sequence constructed demonstrates strong convergence to the common solution of the variational inequality and fixed point problem under standard assumptions. In-depth numerical applications are conducted to illustrate theoretical findings and to compare the proposed algorithms with existing approaches.

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Acknowledgement

The first author would like to thank Faculty of Science and Technology and Research and Development Institute, Valaya Alongkorn Rajabhat University under the Royal Patronage Pathun Thani Province. The second author was supported by University of Phayao and Thailand Science Research and Innovation Fund (Fundamental Fund 2024). The fourth author would like to thank Professor Dr. Poom Kumam from King Mongkuts University of Technology Thonburi, Thailand for his advice and comments to improve the results of this paper. This research (Grant No. RGNS 65-168) was supported by Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation (OPS MHESI), Thailand Science Research and Innovation (TSRI) and Phetchabun Rajabhat University.

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