scholarly journals A general vector-valued variational inequality and its fuzzy extension

1998 ◽  
Vol 21 (4) ◽  
pp. 637-642 ◽  
Author(s):  
Sehie Park ◽  
Byung-Soo Lee ◽  
Gue Myung Lee
Keyword(s):  
Variational Inequality ◽  
Existence Theorem ◽  
Kkm Theorem ◽  
Vector Valued ◽  
General Vector

A general vector-valued variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form of KKM theorem due to Park. Moreover, we obtain the fuzzy extension of our existence theorem.

scholarly journals Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tao Chen
Keyword(s):  
Saddle Point ◽  
Existence Theorem ◽  
Equilibrium Problem ◽  
Existence Result ◽  
Existence Theorems ◽  
Saddle Points ◽  
Vector Equilibrium Problem ◽  
Saddle Point Theorem ◽  
Vector Equilibrium ◽  
Vector Valued

A new existence result ofε-vector equilibrium problem is first obtained. Then, by using the existence theorem ofε-vector equilibrium problem, a weaklyε-cone saddle point theorem is also obtained for vector-valued mappings.

A General Vector-Valued Beurling Theorem

2016 ◽  
Vol 86 (3) ◽  
pp. 321-332
Author(s):  
Yanni Chen ◽  
Don Hadwin ◽  
Ye Zhang
Keyword(s):  
Beurling Theorem ◽  
Vector Valued ◽  
General Vector

scholarly journals Vector Variational Inequalities In G-Convex Spaces

2021 ◽  
Vol 53 ◽  
Author(s):  
Maryam Salehnejad ◽  
Mahdi Azhini
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Kkm Theorem ◽  
Convex Spaces

Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces.

The Equilibrium Existence Theorem for Systems of General Quasiequilibrium Problems in GFC-Spaces

2014 ◽  
Vol 556-562 ◽  
pp. 4128-4132
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Kkm Mapping ◽  
Kkm Theorem ◽  
Equilibrium Existence ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Matching Theorem ◽  
Element Theorem

In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

Quasi-free stochastic integral representation theorems over the CCR

1988 ◽  
Vol 104 (2) ◽  
pp. 383-398 ◽  
Author(s):  
Ivan F. Wilde
Keyword(s):  
Hilbert Space ◽  
Integral Representation ◽  
Stochastic Integral ◽  
Stochastic Integrals ◽  
Representation Theorems ◽  
Martingale Representation ◽  
Stochastic Integral Representation ◽  
Vector Valued ◽  
General Vector

AbstractIt is shown that each vector in the Hilbert space of certain quasi-free representations of the CCR can be written uniquely in terms of quantum stochastic integrals. As a consequence, we obtain general vector-valued and operator-valued boson quantum martingale representation theorems.

scholarly journals A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zezhong Wu ◽  
Jiuping Xu
Keyword(s):  
Genetic Algorithm ◽  
Variational Inequality ◽  
Existence Theorem ◽  
Existence Of A Solution ◽  
Method Of Solution

Invex monotonicity and pseudoinvex monotonicity of fuzzy mappings are introduced in this paper, and relations are discussed between invex monotonicity (pseudoinvex monotonicity) and invexity (pseudoinvexity) of fuzzy mappings. The existence of a solution to the fuzzy variational-like inequality is discussed, and the existence theorem can be achieved. Furthermore, some extended properties of the fuzzy variational-like inequality are researched. Finally, method of solution is discussed based on genetic algorithm.

scholarly journals A System of Generalized Variational-Hemivariational Inequalities with Set-Valued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhi-bin Liu ◽  
Jian-hong Gou ◽  
Yi-bin Xiao ◽  
Xue-song Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Directional Derivatives ◽  
Hemivariational Inequalities ◽  
Kkm Theorem ◽  
Special Cases ◽  
Generalized Directional Derivatives ◽  
Set Valued Mappings

By using surjectivity theorem of pseudomonotone and coercive operators rather than the KKM theorem and fixed point theorem used in recent literatures, we obtain some conditions under which a system of generalized variational-hemivariational inequalities concerning set-valued mappings, which includes as special cases many problems of hemivariational inequalities studied in recent literatures, is solvable. As an application, we prove an existence theorem of solutions for a system of generalized variational-hemivariational inequalities involving integrals of Clarke's generalized directional derivatives.

scholarly journals Variational-like inequalities for n-dimensional fuzzy-vector-valued functions and fuzzy optimization

2019 ◽  
Vol 17 (1) ◽  
pp. 627-645
Author(s):  
Ting Xie ◽  
Zengtai Gong
Keyword(s):  
Variational Inequality ◽  
Fuzzy Number ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Decomposition Theorem ◽  
Variational Inequality Problems ◽  
Multiobjective Optimization Problems ◽  
Vector Valued Functions ◽  
The Relationship ◽  
Vector Valued

Abstract The existing results on the variational inequality problems for fuzzy mappings and their applications were based on Zadeh’s decomposition theorem and were formally characterized by the precise sets which are the fuzzy mappings’ cut sets directly. That is, the existence of the fuzzy variational inequality problems in essence has not been solved. In this paper, the fuzzy variational-like inequality problems is incorporated into the framework of n-dimensional fuzzy number space by means of the new ordering of two n-dimensional fuzzy-number-valued functions we proposed [Fuzzy Sets and Systems 295 (2016) 19-36]. As a theoretical basis, the existence and the basic properties of the fuzzy variational inequality problems are discussed. Furthermore, the relationship between the variational-like inequality problems and the fuzzy optimization problems is discussed. Finally, we investigate the optimality conditions for the fuzzy multiobjective optimization problems.

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