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Journal of Global Optimization

, Volume 54, Issue 1, pp 101–116 | Cite as

Strong convergence theorems for variational inequality problems and quasi-\({\phi}\)-asymptotically nonexpansive mappings

  • H. Zegeye
  • N. Shahzad
Article

Abstract

In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-\({\phi}\)-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings.

Keywords

Generalized projection γ-Inverse strongly monotone mappings Monotone mappings Strong convergence Variational inequality problems 

Mathematics Subject Classification (2000)

47H05 47J05 47J25 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Departement of MathematicsUniversity of BotswanaGaboroneBotswana
  2. 2.Department of MathematicsKing Abdul Aziz UniversityJeddahSaudi Arabia

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