scholarly journals Multivalued Variational Inequalities with -Pseudomonotone Mappings in Reflexive Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
A. M. Saddeek ◽  
S. A. Ahmed
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Complementarity Problem ◽  
Nonlinear Complementarity Problem ◽  
Reflexive Banach Spaces ◽  
Nonlinear Complementarity ◽  
Pseudomonotone Mappings ◽  
Multivalued Variational Inequalities

This paper is concerned with the study of a class of variational inequalities with multivalued -pseudomonotone mappings in reflexive Banach spaces by using the -antiresolvent technique. An application to the multivalued nonlinear -complementarity problem is also presented. The results coincide with the corresponding results announced by many others for the gradient state.

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

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