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

Nguyen Ngoc Hai (), Le Dung Muu () and Bui Dinh ()
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Nguyen Ngoc Hai: Trade Union University
Le Dung Muu: VAST
Bui Dinh: Le Quy Don Technical University

Mathematical Methods of Operations Research, 2023, vol. 98, issue 2, No 6, 299-324

Abstract: 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.

Keywords: Common solution; Equilibria; Quasiconvexity; Normal subgradient; Asymptotically nonexpansive; Fixed point; Walras model (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00837-w

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