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 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 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 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 Sensitivity analysis for a new class of generalized parametric nonlinear ordered variational inequality problems in ordered Banach spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Mohd. Sarfaraz ◽  
Ahmed Morsy ◽  
Md. Kalimuddin Ahmad
Keyword(s):  
Sensitivity Analysis ◽  
Variational Inequality ◽  
Banach Spaces ◽  
Existence Result ◽  
Variational Inequality Problems ◽  
New Class ◽  
Special Cases ◽  
Ordered Banach Spaces

Abstract In this study, we introduce a class of new generalized parametric nonlinear ordered variational inequality problems and discuss its existence result. Also, we prove the sensitivity of the solution for the parametric inequality class with the help of B-restricted-accretive method in ordered Banach spaces. Some special cases of the main results are also discussed.

scholarly journals ωb-Topological Vector Spaces

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Vector Spaces ◽  
Closed Set ◽  
Topological Vector Spaces ◽  
New Class ◽  
Fundamental Properties ◽  
General Properties

The purpose of the present paper is to introduce the new class of ω b - topological vector spaces. We study several basic and fundamental properties of ω b - topological and investigate their relationships with certain existing spaces. Along with other results, we prove that transformation of an open (resp. closed) set in aω b - topological vector space is ω b - open (resp. closed). In addition, some important and useful characterizations of ω b - topological vector spaces are established. We also introduce the notion of almost ω b - topological vector spaces and present several general properties of almost ω b - topological vector spaces.

scholarly journals M – STAR – Irresolute Topological Vector Spaces

2021 ◽  
Vol 7 ◽  
pp. 20-36
Author(s):  
Raja Mohammad Latif
Keyword(s):  
Vector Space ◽  
Extreme Point ◽  
Topological Vector Space ◽  
Convex Subset ◽  
Hausdorff Space ◽  
Vector Spaces ◽  
Topological Spaces ◽  
Topological Vector Spaces ◽  
New Class

In 2016 A. Devika and A. Thilagavathi introduced a new class of sets called M*-open sets and investigated some properties of these sets in topological spaces. In this paper, we introduce and study a new class of spaces, namely M*-irresolute topological vector spaces via M*-open sets. We explore and investigate several properties and characterizations of this new notion of M*-irresolute topological vector space. We give several characterizations of M*-Hausdorff space. Moreover, we show that the extreme point of the convex subset of M*-irresolute topological vector space X lies on the boundary.

scholarly journals Existence Results for New Weak and Strong Mixed Vector Equilibrium Problems on Noncompact Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ali Farajzadeh ◽  
Kasamsuk Ungchittrakool ◽  
Apisit Jarernsuk
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Vector Variational Inequality ◽  
Vector Equilibrium Problem ◽  
Variational Inequality Problems ◽  
Vector Equilibrium Problems ◽  
Noncompact Domain ◽  
Vector Equilibrium

We introduce and consider two new mixed vector equilibrium problems, that is, a new weak mixed vector equilibrium problem and a new strong mixed vector equilibrium problem which are combinations of certain vector equilibrium problems, and vector variational inequality problems. We prove existence results for the problems in noncompact setting.

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