链完备偏序集上广义向量均衡问题解映射的保序性

Abstract

Abstract:

In this paper, we explore the upper order-preservation of solution correspondence for parametric generalized vector equilibrium problems on chain-complete posets. In contrast to the previous results which mainly focus on the existence, topological continuity and algorithms, the order-preservation is a new subject for generalized vector equilibrium problems and it is useful for predicting the changing trend of solutions. Since our approaches are order-theoretic fixed point theorems and isotone selection theorems, neither convexity nor continuity is required for the mapping F.

Key words: Chain-complete poset, Generalized vector equilibrium problems, Fixed point theorem, Order-preservation

CLC Number:

Yuehu Wang,Baoqing Liu. Order-Preservation of Solution Correspondence for Generalized Vector Equilibrium Problems on Chain-Complete Posets[J].Acta mathematica scientia,Series A, 2019, 39(6): 1483-1491.

Trendmd

References 24

1	Ansari Q H , Oettli W , Schläger D . A generalization of vectorial equilibria. Math Method Oper Res, 1997, 46 (2): 147- 152
2	Chadli O , Chiang Y , Huang S . Topological pseudomonotonicity and vector equilibrium problems. J Math Anal Appl, 2002, 270 (2): 435- 450
3	Li J , Huang N J , Kim J . On implicit vector equilibrium problems. J Math Anal Appl, 2003, 283 (2): 501- 512
4	Farajzadeh A P , Amini-Harandi A . On the generalized vector equilibrium problems. J Math Anal Appl, 2008, 344 (2): 999- 1004
5	Capǎtǎ A . Exisrence results for globally efficient solutions of vector equilibrium problems via a generalized KKM principle. Acta Math Sci, 2017, 37 (2): 463- 476 doi: 10.1016/S0252-9602(17)30014-0
6	Ansari Q H , Konnov I V , Yao J C . On generalized vector equilibrium problems. Acta Math Appl Sin, 2006, 47 (1): 543- 554
7	Ansari Q H , Schaible S , Yao J C . The system of generalized vector equilibrium problems with applications. J Global Optim, 2002, 22 (1/4): 3- 16
8	Ansari Q H , Flores-Bazan F . Generalized vector quasi-equilibrium problems with applications. J Math Anal Appl, 2003, 277 (1): 246- 256 doi: 10.1016/S0022-247X(02)00535-8
9	Lashkaripour R , Karamian A . On a new generalized symmetric vector equilibrium problem. J Inequal Appl, 2017, 2017 (1): 237
10	Bianchi M , Kassay G , Pini R . Ekeland's principle for vector equilibrium problems. Nonlinear Analysis, 2007, 66 (7): 1454- 1464
11	Gong X . Ekeland's principle for set-valued vector equilibrium problems. Acta Math Sci, 2014, 34 (4): 1179- 1192
12	Gutiérrez C , Kassay G , Novo V , Ródenas-Pedregosa J L . Ekeland variational principles in vector equilibrium problems. SIAM J Optimiz, 2017, 27 (4): 2405- 2425 doi: 10.1137/17M111883X
13	Göpfert A , Riahi H , Tammer C , et al. Variational Methods in Partially Ordered Spaces. New York: Springer, 2003
14	Nishimura H , Ok E A . Solvability of variational inequalities on Hilbert lattices. Math Oper Res, 2012, 37 (4): 608- 625
15	Xie L , Li J , Yang W . Order-clustered fixed point theorems on chain-complete preordered sets and their applications to extended and generalized Nash equilibria. Fixed Point Theory A, 2013, 2013 (1): 192
16	Zhang C , Wang Y . Applications of order-theoretic fixed points theorems to discontinuous quasi-equilibrium problems. Fixed Point Theory A, 2015, 2015: 54 doi: 10.1186/s13663-015-0306-5
17	Meyer-Nieberg P . Banach Lattices. Berlin: Springer-Verlag, 1991
18	Löhne A . Vector Optimization with Infimum and Supremum. Heidelberg: Springer, 2011
19	Kukushkin N S . Increasing selections from increasing multifunctions. Order, 2013, 30 (2): 541- 555
20	Li J . Several extensions of the Abian-Brown fixed point theorem and their applications to extended and generalized Nash equilibria on chain-complete posets. J Math Anal Appl, 2014, 409 (2): 1084- 1092 doi: 10.1016/j.jmaa.2013.07.070
21	Smithson R E . Fixed points of order preserving multifunctions. Proc Amer Math Soc, 1971, 28 (1): 304- 310
22	Abian S , Brown A B . A theorem on partially ordered sets, with applications to fixed point theorems. Can J Math, 1961, 13: 78- 82
23	Tarski A . A lattice-theoretical fixpoint theorem and its applications. Pac J Math, 1955, 5 (2): 285- 309
24	Wang Y , Zhang C . Order-preservations of solution correspondence for parametric generalized variational inequalities on Banach lattices. Fixed Point Theory and Applications, 2015, 2015: 108 doi: 10.1186/s13663-015-0360-z

[1]	Gao Chenghua, Ding Huanhuan, He Xingyue. Radial Solutions of Coupled Systems for a Class of Superlinear $ k$-Hessian Equations [J]. Acta mathematica scientia,Series A, 2024, 44(2): 384-395.
[2]	Zhang Guangxin, Yang Yunrui, Song Xue. Periodic Traveling Wave Solutions of Delayed SEIR Systems with Nonlocal Effects [J]. Acta mathematica scientia,Series A, 2024, 44(1): 140-159.
[3]	Song Yuying, Fan Hongxia. Existence and Regularity of Solutions for a Class of Neutral Stochastic Evolution Equations [J]. Acta mathematica scientia,Series A, 2023, 43(1): 238-248.
[4]	Wenjie Liu,Shengli Xie. Existence Results of Mild Solutions for Impulsive Neutral Measure Differential Equations with Infinite Delay [J]. Acta mathematica scientia,Series A, 2022, 42(6): 1671-1681.
[5]	Lei Duan,Tianlan Chen. Existence of Convex Solutions for a Discrete Mixed Boundary Value Problem with the Mean Curvature Operator [J]. Acta mathematica scientia,Series A, 2022, 42(2): 379-386.
[6]	Xiaoling Han,Huize Cai,Hujun Yang. Existence and Uniqueness of Solutions for the Boundary Value Problems of Nonlinear Fractional Differential Equations on Star Graph [J]. Acta mathematica scientia,Series A, 2022, 42(1): 139-156.
[7]	Jifeng Zhang,Wei Zhang,Jinbo Ni,Dandan Ren. Existence of Solutions for Anti-Periodic Boundary Value Problems of Fractional Langevin Equation with p(t)-Laplacian Operator [J]. Acta mathematica scientia,Series A, 2021, 41(4): 1024-1032.
[8]	Zaitao Liang,Xuemeng Shan. Multiplicity of Radial Solutions of $ k$-Hessian Equations [J]. Acta mathematica scientia,Series A, 2021, 41(1): 63-68.
[9]	Yan Luo,Wenzhe Xie. Existence of Solutions for Impulsive Differential Inclusions with Upper and Lower Solutions in the Reverse Order [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1055-1063.
[10]	Xiaohang Ou. Sufficient and Necessary Condition for the Existence of Positive Entire Solutions of a Nonlinear Biharmonic Equations on ${{\mathbb{R}}^{N}}$ [J]. Acta mathematica scientia,Series A, 2019, 39(3): 535-544.
[11]	Bo Zhu,Lishan Liu. Existence and Uniqueness of the Mild Solutions for a Class of Fractional Non-Autonomous Evolution Equations with Impulses [J]. Acta mathematica scientia,Series A, 2019, 39(1): 105-113.
[12]	Zou Xia, Wu Shiliang. Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence [J]. Acta mathematica scientia,Series A, 2018, 38(3): 496-513.
[13]	Guo Tingguang, Xu Zhiting. Existence of Traveling Waves in a Spatial Infectious Disease Model with Vaccination [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1129-1147.
[14]	Diem Dang Huan, Gao Hongjun. Well-Posedness for Fractional Neutral Impulsive Stochastic Integro-Differential Equations [J]. Acta mathematica scientia,Series A, 2015, 35(2): 405-421.
[15]	Dumitru MOTREANU, Abdelkrim MOUSSAOUI. A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE [J]. Acta mathematica scientia,Series A, 2014, 34(3): 905-916.

Order-Preservation of Solution Correspondence for Generalized Vector Equilibrium Problems on Chain-Complete Posets

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 24

Related Articles 15

Metrics

Comments

Recommended 10