scholarly journals Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1801-1810
Author(s):  
Mohammad Chowdhury ◽  
Cho Yeol
Keyword(s):  
Variational Inequalities ◽  
Existence Results ◽  
Vector Spaces ◽  
Type Ii ◽  
Topological Vector Spaces ◽  
New Class ◽  
Locally Convex ◽  
Monotone Type

In this paper, we introduce a new class of generalized bi-quasi-variational inequalities for quasipseudo- monotone type II operators in non-compact settings of locally convex Hausdorff topological vector spaces and show the existence results of solutions for generalized bi-quasi-variational inequalities. Our results improve, extend and generalized the corresponding results given by some authors

scholarly journals A class of nonlinear variational inequalities involving pseudomonotone operators

2000 ◽  
Vol 13 (1) ◽  
pp. 73-75
Author(s):  
Ram U. Verma
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Monotone Operators ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Pseudomonotone Operators ◽  
Topological Vector Spaces ◽  
Locally Convex

We present the solvability of a class of nonlinear variational inequalities involving pseudomonotone operators in a locally convex Hausdorff topological vector spaces setting. The obtained result generalizes similar variational inequality problems on monotone operators.

scholarly journals GENERALIZED MIXED QUASI-COMPLEMENTARITY PROBLEMS IN TOPOLOGICAL VECTOR SPACES

2008 ◽  
Vol 49 (4) ◽  
pp. 525-531
Author(s):  
ALI P. FRAJZADEH ◽  
MUHAMMAD ASLAM NOOR
Keyword(s):  
Variational Inequalities ◽  
Vector Space ◽  
Complementarity Problems ◽  
Vector Spaces ◽  
Kkm Mapping ◽  
Existence Of A Solution ◽  
Topological Vector Spaces ◽  
New Class ◽  
Special Cases ◽  
New Type

AbstractIn this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solution of the generalized mixed quasi-variational inequalities and generalized mixed quasi-complementarity problems. Several special cases are also discussed. The results obtained in this paper can be viewed as extension and generalization of the previously known results.

scholarly journals GENERALIZED IMPLICIT INCLUSION PROBLEMS ON NONCOMPACT SETS WITH APPLICATIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 261-279
Author(s):  
SAN-HUA WANG ◽  
NAN-JING HUANG
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Existence Results ◽  
Vector Spaces ◽  
Vector Equilibrium Problems ◽  
Inclusion Problems ◽  
Topological Vector Spaces ◽  
Vector Equilibrium

AbstractIn this paper, a class of generalized implicit inclusion problems is introduced, which can be regarded as a generalization of variational inequality problems, equilibrium problems, optimization problems and inclusion problems. Some existence results of solutions for such problems are obtained on noncompact subsets of Hausdorff topological vector spaces using the famous FKKM theorem. As applications, some existence results for vector equilibrium problems and vector variational inequalities on noncompact sets of Hausdorff topological vector spaces are given.

scholarly journals A new class of bilevel weak vector variational inequality problems

2020 ◽  
pp. 321-331
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Vector Variational Inequality ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
New Class ◽  
Existence Conditions ◽  
Locally Convex ◽  
Weak Vector

In this paper, we first introduce a new class of bilevel weak vector variational inequality problems in locally convex Hausdorff topological vector spaces. Then, using the Kakutani-Fan-Glicksberg fixed-point theorem, we establish some existence conditions of the solution for this problem.

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

scholarly journals ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS

2008 ◽  
Vol 50 (2) ◽  
pp. 271-288
Author(s):  
HELGE GLÖCKNER
Keyword(s):  
Differential Calculus ◽  
Vector Spaces ◽  
Local Convexity ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
General Curve ◽  
Infinite Dimensional Analysis ◽  
Locally Convex ◽  
Differentiability Properties ◽  
Made In

AbstractThe General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. In this article, we generalize the General Curve Lemma in two ways. First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.

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