Journal of Global Optimization

, Volume 54, Issue 1, pp 173–184

Strong convergence of an iterative method for pseudo-contractive and monotone mappings


DOI: 10.1007/s10898-011-9755-5

Cite this article as:
Zegeye, H. & Shahzad, N. J Glob Optim (2012) 54: 173. doi:10.1007/s10898-011-9755-5


In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive mapping and solutions of variational inequality problem for monotone mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive mappings and solutions set of finite family of variational inequality problems for continuous monotone mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.


Monotone mappings Nonexpansive mappings Pseudocontractive mappings 

Mathematics Subject Classification (2000)

47H05 47J05 47J25 

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

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

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