Pseudomonotone Maps: Properties and Applications

2008 ◽  
pp. 3105-3110
Author(s):  
Nicolas Hadjisavvas
Keyword(s):  
Pseudomonotone Maps

SET-VALUED PSEUDOMONOTONE MAPS AND DEGENERATE EVOLUTION INCLUSIONS

1999 ◽  
Vol 01 (01) ◽  
pp. 87-123 ◽  
Author(s):  
KENNETH L. KUTTLER ◽  
MEIR SHILLOR
Keyword(s):  
Weak Solution ◽  
Friction Coefficient ◽  
Frictional Contact ◽  
Contact Problems ◽  
Pseudomonotone Operator ◽  
Unique Weak Solution ◽  
Dynamical Models ◽  
Evolution Inclusions ◽  
Theory Of Evolution ◽  
Pseudomonotone Maps

We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are [Formula: see text] where B=B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems.We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution.This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.

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 Variational-Like Inequalities and Equilibrium Problems with Generalized Monotonicity in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
N. K. Mahato ◽  
C. Nahak
Keyword(s):  
Equilibrium Problem ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
Generalized Monotonicity ◽  
Reflexive Banach Spaces ◽  
Strong Pseudomonotonicity ◽  
Pseudomonotone Maps ◽  
Pseudomonotone Mappings

We introduce the notion of relaxed (ρ-θ)-η-invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed (ρ-θ)-η-invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of (ρ-θ)-pseudomonotonicity for bifunctions, and we consider some examples to show that (ρ-θ)-pseudomonotonicity generalizes both monotonicity and strong pseudomonotonicity. The existence of solution for equilibrium problem with (ρ-θ)-pseudomonotone mappings in reflexive Banach spaces are demonstrated by using the KKM technique.

Integration of pseudomonotone maps and the revealed preference problem

Optimization ◽  
2010 ◽  
Vol 60 (7) ◽  
pp. 783-800 ◽  
Author(s):  
Jean-Pierre Crouzeix ◽  
Abdelkrim Keraghel ◽  
Nadia Rahmani
Keyword(s):  
Revealed Preference ◽  
Pseudomonotone Maps
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