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.

scholarly journals Nonlinear Vector Variational Inequality Problems for η-Pseudomonotone Maps

2007 ◽  
Vol 2007 ◽  
pp. 1-6
Author(s):  
A. P. Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Existence Result ◽  
Complementarity Problems ◽  
Vector Variational Inequality ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
New Class ◽  
Pseudomonotone Maps ◽  
Nonlinear Vector

We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an existence result for their solutions in real Hausdorff topological vector spaces. Our results extend the same previous results in this literature.

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 Variational inequality problems inH-spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-18
Author(s):  
Akrur Behera ◽  
Prasanta Kumar Das
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Complementarity Problem ◽  
Vector Variational Inequality ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Lefschetz Number ◽  
Topological Vector Spaces ◽  
Invex Set ◽  
Invex Function

The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended toH-spaces and differentiablen-manifolds. The solution of complementarity problem is also studied in the presence of fixed points or Lefschetz number.

scholarly journals Vector and Ordered Variational Inequalities and Applications to Order-Optimization Problems on Banach Lattices

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Linsen Xie ◽  
Jinlu Li ◽  
Wenshan Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Point Theorems ◽  
Optimization Problems ◽  
Banach Lattices ◽  
Variational Inequality Problems ◽  
Vector Spaces ◽  
Real Vector ◽  
Finite Dimensional

We investigate the connections between vector variational inequalities and ordered variational inequalities in finite dimensional real vector spaces. We also use some fixed point theorems to prove the solvability of ordered variational inequality problems and their application to some order-optimization problems on the Banach lattices.

FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES

2011 ◽  
Vol 04 (03) ◽  
pp. 373-387 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Vector Spaces ◽  
Compact Sets ◽  
Multivalued Maps ◽  
Weakly Compact ◽  
Topological Vector Spaces ◽  
Admissible Maps ◽  
Weakly Compact Sets ◽  
Locally Convex

We present new fixed point theorems for multivalued [Formula: see text]-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

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 Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals Some new deterministic and random variational inequalities and their applications

1995 ◽  
Vol 8 (4) ◽  
pp. 381-391 ◽  
Author(s):  
Xian-Zhi Yuan ◽  
Jean-Marc Roy
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Best Approximation ◽  
Fixed Point Theorems ◽  
Approximation Theorem ◽  
Saddle Points ◽  
Vector Spaces ◽  
Random Fixed Point ◽  
Topological Vector Spaces ◽  
Random Variational Inequalities

A non-compact deterministic variational inequality which is used to prove an existence theorem for saddle points in the setting of topological vector spaces and a random variational inequality. The latter result is then applied to obtain the random version of the Fan's best approximation theorem. Several random fixed point theorems are obtained as applications of the random best approximation theorem.

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