Ranges of operators and convex variational inequalities. (1st January 2013)

• Record Type: Journal Article
• Authors: Garralda-Guillem, Ana Isabel; Ruiz Galán, Manuel
• Is Part Of: International journal of applied nonlinear science. Volume 1:Number 1(2013)
• Page Start: 52
• Page End: 66
• Publication Date: 2013-01-01
• Subjects: range of an operator -- minimax inequalities -- variational principles -- Galerkin methods -- bases -- reflexivity; Science -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; Nonlinear theories -- Periodicals; 501.5118
• Languages: English
• ISSNs: 1752-2862

Abstract

The main topic in this work is the analysis of the range of a continuous and linear operator between Banach spaces, approached here through non-linear techniques, more precisely, by means of the classical Fan minimax theorem. We characterise the elements in the range of such an operator as those satisfying a certain variational inequality and provide a numerical scheme of Galerkin type to determine approximately the preimage of an element that lies in that range. The passage from the theoretical setting to its numerical realisation is done by means of the use of bases in adequate spaces. In addition we deal with the extension of the previous results to the case of systems of variational inequalities.