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

被引：1

作者：

Hai, Nguyen Ngoc ^{[1
]}

Muu, Le Dung ^{[2
,3
]}

Dinh, Bui Van ^{[4
]}

机构：

[1] Trade Union Univ, Hanoi, Vietnam

[2] Thang Long Univ, TIMAS, Hanoi, Vietnam

[3] VAST, Inst Math, Hanoi, Vietnam

[4] Le Quy Don Tech Univ, Dept Math, Hanoi, Vietnam

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2023年 / 98卷 / 02期

关键词：

Common solution; Equilibria; Quasiconvexity; Normal subgradient; Asymptotically nonexpansive; Fixed point; Walras model; STRONG-CONVERGENCE THEOREMS; KY FAN INEQUALITIES; FIXED-POINTS; EXTRAGRADIENT METHODS; SUBGRADIENT METHODS; APPROXIMATION; WEAK;

D O I：

10.1007/s00186-023-00837-w

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：299 / 324

页数：26

共 46 条

[1]

AGARWAL R.P., 2000, Fixed Point Theory for Lipschitzian-type Mappings with Applications

[2] EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY [J].