Acta Applicandae Mathematicae

, Volume 110, Issue 1, pp 227–246

On General Mixed Variational Inequalities

  • Muhammad Aslam Noor
  • Khalida Inayat Noor
  • Huma Yaqoob
Article

DOI: 10.1007/s10440-008-9402-4

Cite this article as:
Aslam Noor, M., Inayat Noor, K. & Yaqoob, H. Acta Appl Math (2010) 110: 227. doi:10.1007/s10440-008-9402-4

Abstract

In this paper, we introduce and consider a new class of mixed variational inequalities, which is called the general mixed variational inequality. Using the resolvent operator technique, we establish the equivalence between the general mixed variational inequalities and the fixed-point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving the general mixed variational inequalities. We study the convergence criteria of the suggested iterative methods under suitable conditions. Using the resolvent operator technique, we also consider the resolvent dynamical systems associated with the general mixed variational inequalities. We show that the trajectory of the dynamical system converges globally exponentially to the unique solution of the general mixed variational inequalities. Our methods of proofs are very simple as compared with others’ techniques. Results proved in this paper may be viewed as a refinement and important generalizations of the previous known results.

Keywords

Variational inequalities Nonconvex functions Fixed-point problem Resolvent operator Resolvent equations Projection operator Convergence Dynamical systems 

Mathematics Subject Classification (2000)

49J40 90C33 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Muhammad Aslam Noor
    • 1
  • Khalida Inayat Noor
    • 1
  • Huma Yaqoob
    • 1
  1. 1.Mathematics DepartmentCOMSATS Institute of Information TechnologyIslamabadPakistan

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