Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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APPROXIMATE PROJECTION ALGORITHMS FOR SOLVING EQUILIBRIUM AND MULTIVALUED VARIATIONAL INEQUALITY PROBLEMS IN HILBERT SPACE

  • Received : 2021.08.15
  • Accepted : 2022.02.23
  • Published : 2022.07.31
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Abstract

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

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Acknowledgement

The authors would like to thank the Editor and the referees for their comments on the manuscript which helped in improving earlier version of this paper.

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