Journal of Applied Mathematics and Computing

, Volume 32, Issue 1, pp 83–95

Projection iterative methods for extended general variational inequalities


DOI: 10.1007/s12190-009-0234-9

Cite this article as:
Noor, M.A. J. Appl. Math. Comput. (2010) 32: 83. doi:10.1007/s12190-009-0234-9


In this paper, we introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.


Variational inclusions Fixed point problems Wiener-Hopf equations Nonlinear operators Convergence criteria 

Mathematics Subject Classification (2000)

49J40 90C33 

Copyright information

© Korean Society for Computational and Applied Mathematics 2009

Authors and Affiliations

  1. 1.Mathematics DepartmentCOMSATS Institute of Information TechnologyIslamabadPakistan

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