minimax inequality
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Author(s):  
Marco Castellani ◽  
Massimiliano Giuli

AbstractAn existence result for a generalized inequality over a possible unbounded domain in a finite-dimensional space is established. The proof technique allows to avoid any monotonicity assumption. We adapt a weak coercivity condition introduced in Castellani and Giuli (J Glob Optim 75:163–176, 2019) for a generalized game which extends an older one proposed by Konnov and Dyabilkin (J Glob Optim 49:575–577, 2011) for equilibrium problems. Our main result encompasses and generalizes several existence results for equilibrium, quasiequilibrium and fixed-point problems.



2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Haiyan Gao ◽  
Lili Wang ◽  
Liangshi Zhao

Abstract This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fixed point theorem, and FanKKM theorem, we obtain a sufficient condition which guarantees the existence of solutions for the generalized nonlinear variational-like inequality. We introduce also an auxiliary variational-like inequality and, by utilizing the minimax inequality, get the existence and uniqueness of solutions for the auxiliary variational-like inequality, which is used to suggest an iterative algorithm for solving the generalized nonlinear variational-like inequality. Under certain conditions, by means of the auxiliary principle technique, we both establish the existence and uniqueness of solutions for the generalized nonlinear variational-like inequality and discuss the convergence of iterative sequences generated by the iterative algorithm. Our results extend, improve, and unify several known results in the literature.



2020 ◽  
Vol 49 (4) ◽  
pp. 1143-1153
Author(s):  
Achille Basile ◽  
Vincenzo Scalzo

AbstractWe give sufficient and necessary conditions for the non-emptiness of the alpha-core in the setting of strategic games with non-ordered and discontinuous preferences. In order to prove our results, we can avoid the use of Scarf’s Theorem for NTU-games, by suitably appealing to the Ky Fan minimax inequality. Examples clarify our conditions and allow the comparison of our results with the previous ones.



2018 ◽  
Vol 179 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Marco Castellani ◽  
Massimiliano Giuli ◽  
Massimo Pappalardo


Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1307-1313
Author(s):  
Nasrin Karamikabir ◽  
Abdolrahman Razani

In this paper, a coincidence theorem is obtained which is generalization of Ky Fan?s fixed point theorem in modular function spaces. A modular version of Fan?s minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.



2013 ◽  
Vol 838-841 ◽  
pp. 2219-2222
Author(s):  
He Rui Li ◽  
Kai Ting Wen

In this paper, MFC mappings is introduced and Ky Fan matching theorems for MFC mappings with transfer compactly open values are established in noncompact complete FC-metric spaces. As applications, a Fan-Browder type coincidence theorem and a minimax inequality are obtained. Our results unify, improve and generalize some known results in recent literature.



2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Shuwen Xiang ◽  
Shunyou Xia ◽  
Jing Chen


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