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Abstract

The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others as special cases. This paper presents a picture for the relationship between the fixed points of the Moreau proximal mapping and the solutions of the equilibrium problem that satisfies some kinds of monotonicity and Lipschitz-type condition.

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Acknowledgements

The authors are grateful to the editor and anonymous reviewers for insightful comments and suggestions, that help improve the presentation of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.06.

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Correspondence to Xuan Thanh Le.

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Muu, L.D., Le, X.T. On fixed point approach to equilibrium problem. J. Fixed Point Theory Appl. 23, 50 (2021). https://doi.org/10.1007/s11784-021-00890-0

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