Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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A MODIFIED KRASNOSELSKII-TYPE SUBGRADIENT EXTRAGRADIENT ALGORITHM WITH INERTIAL EFFECTS FOR SOLVING VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEM

  • Araya Kheawborisut (Department of Mathematics, School of Science, King Mongkut's Institute of Technology Ladkrabang) ;
  • Wongvisarut Khuangsatung (Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi)
  • Received : 2023.05.15
  • Accepted : 2024.02.12
  • Published : 2024.06.15
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Abstract

In this paper, we propose a new inertial subgradient extragradient algorithm with a new linesearch technique that combines the inertial subgradient extragradient algorithm and the KrasnoselskiiMann algorithm. Under some suitable conditions, we prove a weak convergence theorem of the proposed algorithm for finding a common element of the common solution set of a finitely many variational inequality problem and the fixed point set of a nonexpansive mapping in real Hilbert spaces. Moreover, using our main result, we derive some others involving systems of variational inequalities. Finally, we give some numerical examples to support our main result.

Keywords

Acknowledgement

The second author would like to thank Rajamangala University of Technology Thanyaburi (RMUTT) under The Science, Research and Innovation Promotion Funding (TSRI) (Contract No. FRB660012/0168 and under project number FRB66E0635) for financial support.

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