Journal of Optimization Theory and Applications

, Volume 121, Issue 1, pp 203–210

Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods

  • R. U. Verma
Note

DOI: 10.1023/B:JOTA.0000026271.19947.05

Cite this article as:
Verma, R.U. Journal of Optimization Theory and Applications (2004) 121: 203. doi:10.1023/B:JOTA.0000026271.19947.05

Abstract

Let K be a nonempty closed convex subset of a real Hilbert space H. The approximate solvability of a system of nonlinear variational inequality problems, based on the convergence of projection methods, is discussed as follows: find an element (x*, y*)∈K×K such that
$$\begin{gathered} \left\langle {\rho {\rm T}(y^* ,x^* ) + x^* - y^* ,x - x^* } \right\rangle \geqslant 0,{\text{ }}\forall x \in K{\text{ and }}\rho > 0, \hfill \\ \left\langle {\eta {\rm T}(x^* ,y^* ) + y^* - x^* ,x - x^* } \right\rangle \geqslant 0,{\text{ }}\forall x \in K{\text{ and }}\eta > 0, \hfill \\ \end{gathered}$$
where T: K×KH is a nonlinear mapping on K×K.
Relaxed cocoercive nonlinear variational inequalities projection methods relaxed cocoercive mappings cocoercive mappings convergence of projection methods 

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • R. U. Verma
    • 1
  1. 1.Department of MathematicsUniversity of ToledoToledo

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