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An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand

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Abstract

We propose a normal subgradient projection algorithm for approximating a solution of equilibrium problems involving quasiconvex para-pseudomonotone bifunctions, which is also a fixed point of an asymptotically nonexpansive mapping. The proposed algorithm is a combination between a projection one for the equilibrium problem and the Ishikawa iteration scheme for the fixed point. Convergence of the algorithm is proved without any Lipschitz type condition for the bifunction. Applications to a modified Walras equilibrium model with implicit supply and demand are discussed.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study. The readers who are interested in Python codes for examples should contact Bui Van Dinh.

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Acknowledgements

The authors would like to thank the editor in chief, the editors and the referees very much for their constructive comments and suggestions, especially on the sufficient condition for the existence of a common solution of equilibrium and fixed point problems and the presentation of their submitted version. These helped them very much in revising their paper.

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Authors and Affiliations

  1. Trade Union University, Hanoi, Vietnam

    Nguyen Ngoc Hai

  2. TIMAS, Thang Long University and Institute of Mathematics, VAST, Hanoi, Vietnam

    Le Dung Muu

  3. Department of Mathematics, Le Quy Don Technical University, Hanoi, Vietnam

    Bui Van Dinh

Authors
  1. Nguyen Ngoc Hai
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  2. Le Dung Muu
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  3. Bui Van Dinh
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Correspondence to Bui Van Dinh.

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A part of this article was written while the third author was visiting Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the institute for warm hospitality and partial support.

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Hai, N.N., Muu, L.D. & Van Dinh, B. An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand. Math Meth Oper Res 98, 299–324 (2023). https://doi.org/10.1007/s00186-023-00837-w

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  • DOI: https://doi.org/10.1007/s00186-023-00837-w

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