scholarly journals Multiple Existence of Solutions for Nonlinear Variational Inequalities

1994 ◽  
Vol 113 (2) ◽  
pp. 272-299 ◽  
Author(s):  
N. Hirano
Keyword(s):  
Variational Inequalities ◽  
Existence Of Solutions

scholarly journals Minimax theorems in probabilistic metric spaces

1995 ◽  
Vol 51 (1) ◽  
pp. 103-119 ◽  
Author(s):  
Y.J. Cho ◽  
S.S. Chang ◽  
J.S. Jung ◽  
S.M. Kang ◽  
X. Wu
Keyword(s):  
Variational Inequalities ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Minimax Theorems ◽  
Saddle Point Problems ◽  
Coincidence Points ◽  
Probabilistic Metric Spaces ◽  
Upper Semicontinuous Functions ◽  
Probabilistic Metric ◽  
Semicontinuous Functions

In this paper, new minimax theorems for mixed lower-upper semicontinuous functions in probabilistic metric spaces are given. As applications, we utilise these results to show the existence of solutions of abstract variational inequalities, implicit variational inequalities and saddle point problems, and the existence of coincidence points in probabilistic metric spaces.

scholarly journals Some Existence Theorems for Nonconvex Variational Inequalities Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Narin Petrot
Keyword(s):  
Variational Inequalities ◽  
Nonsmooth Analysis ◽  
Existence Of Solutions ◽  
Existence Theorems

By using nonsmooth analysis knowledge, we provide the conditions for existence solutions of the variational inequalities problems in nonconvex setting. We also show that the strongly monotonic assumption of the mapping may not need for the existence of solutions. Consequently, the results presented in this paper can be viewed as an improvement and refinement of some known results from the literature.

scholarly journals On a class of generalized stochastic Browder mixed variational inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Chao Min ◽  
Fei-fei Fan ◽  
Zhao-zhong Yang ◽  
Xiao-gang Li
Keyword(s):  
Variational Inequalities ◽  
Existence Of Solutions ◽  
Uniqueness Of Solution ◽  
Measurable Selection ◽  
Stochastic Variational Inequalities ◽  
Selection Theorem ◽  
Solution Sets ◽  
Mixed Variational Inequalities

AbstractIn this paper, we introduce a class of stochastic variational inequalities generated from the Browder variational inequalities. First, the existence of solutions for these generalized stochastic Browder mixed variational inequalities (GS-BMVI) are investigated based on FKKM theorem and Aummann’s measurable selection theorem. Then the uniqueness of solution for GS-BMVI is proved based on strengthening conditions of monotonicity and convexity, the compactness and convexity of the solution sets are discussed by Minty’s technique. The results of this paper can provide a foundation for further research of a class of stochastic evolutionary problems driven by GS-BMVI.

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